Inférence robuste à la présence des valeurs aberrantes dans les enquêtes

Cette thèse comporte trois articles dont un est publié et deux en préparation. Le sujet central de la thèse porte sur le traitement des valeurs aberrantes représentatives dans deux aspects importants des enquêtes que sont : l’estimation des petits domaines et l’imputation en présence de non-réponse partielle. En ce qui concerne les petits domaines, les estimateurs robustes dans le cadre des modèles au niveau des unités ont été étudiés. Sinha & Rao (2009) proposent une version robuste du meilleur prédicteur linéaire sans biais empirique pour la moyenne des petits domaines. Leur estimateur robuste est de type «plugin», et à la lumière des travaux de Chambers (1986), cet estimateur peut être biaisé dans certaines situations. Chambers et al. (2014) proposent un estimateur corrigé du biais. En outre, un estimateur de l’erreur quadratique moyenne a été associé à ces estimateurs ponctuels. Sinha & Rao (2009) proposent une procédure bootstrap paramétrique pour estimer l’erreur quadratique moyenne. Des méthodes analytiques sont proposées dans Chambers et al. (2014). Cependant, leur validité théorique n’a pas été établie et leurs performances empiriques ne sont pas pleinement satisfaisantes. Ici, nous examinons deux nouvelles approches pour obtenir une version robuste du meilleur prédicteur linéaire sans biais empirique : la première est fondée sur les travaux de Chambers (1986), et la deuxième est basée sur le concept de biais conditionnel comme mesure de l’influence d’une unité de la population. Ces deux classes d’estimateurs robustes des petits domaines incluent également un terme de correction pour le biais. Cependant, ils utilisent tous les deux l’information disponible dans tous les domaines contrairement à celui de Chambers et al. (2014) qui utilise uniquement l’information disponible dans le domaine d’intérêt. Dans certaines situations, un biais non négligeable est possible pour l’estimateur de Sinha & Rao (2009), alors que les estimateurs proposés exhibent un faible biais pour un choix approprié de la fonction d’influence et de la constante de robustesse. Les simulations Monte Carlo sont effectuées, et les comparaisons sont faites entre les estimateurs proposés et ceux de Sinha & Rao (2009) et de Chambers et al. (2014). Les résultats montrent que les estimateurs de Sinha & Rao (2009) et de Chambers et al. (2014) peuvent avoir un biais important, alors que les estimateurs proposés ont une meilleure performance en termes de biais et d’erreur quadratique moyenne. En outre, nous proposons une nouvelle procédure bootstrap pour l’estimation de l’erreur quadratique moyenne des estimateurs robustes des petits domaines. Contrairement aux procédures existantes, nous montrons formellement la validité asymptotique de la méthode bootstrap proposée. Par ailleurs, la méthode proposée est semi-paramétrique, c’est-à-dire, elle n’est pas assujettie à une hypothèse sur les distributions des erreurs ou des effets aléatoires. Ainsi, elle est particulièrement attrayante et plus largement applicable. Nous examinons les performances de notre procédure bootstrap avec les simulations Monte Carlo. Les résultats montrent que notre procédure performe bien et surtout performe mieux que tous les compétiteurs étudiés. Une application de la méthode proposée est illustrée en analysant les données réelles contenant des valeurs aberrantes de Battese, Harter & Fuller (1988). S’agissant de l’imputation en présence de non-réponse partielle, certaines formes d’imputation simple ont été étudiées. L’imputation par la régression déterministe entre les classes, qui inclut l’imputation par le ratio et l’imputation par la moyenne sont souvent utilisées dans les enquêtes. Ces méthodes d’imputation peuvent conduire à des estimateurs imputés biaisés si le modèle d’imputation ou le modèle de non-réponse n’est pas correctement spécifié. Des estimateurs doublement robustes ont été développés dans les années récentes. Ces estimateurs sont sans biais si l’un au moins des modèles d’imputation ou de non-réponse est bien spécifié. Cependant, en présence des valeurs aberrantes, les estimateurs imputés doublement robustes peuvent être très instables. En utilisant le concept de biais conditionnel, nous proposons une version robuste aux valeurs aberrantes de l’estimateur doublement robuste. Les résultats des études par simulations montrent que l’estimateur proposé performe bien pour un choix approprié de la constante de robustesse.

Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

Reliability of a quantitative clinical posture assessment tool among persons with idiopathic scoliosis

Objective To determine overall, test–retest and inter-rater reliability of posture indices among persons with idiopathic scoliosis. Design A reliability study using two raters and two test sessions. Setting Tertiary care paediatric centre. Participants Seventy participants aged between 10 and 20 years with different types of idiopathic scoliosis (Cobb angle 15 to 60°) were recruited from the scoliosis clinic. Main outcome measures Based on the XY co-ordinates of natural reference points (e.g. eyes) as well as markers placed on several anatomical landmarks, 32 angular and linear posture indices taken from digital photographs in the standing position were calculated from a specially developed software program. Generalisability theory served to estimate the reliability and standard error of measurement (SEM) for the overall, test–retest and inter-rater designs. Bland and Altman's method was also used to document agreement between sessions and raters. Results In the random design, dependability coefficients demonstrated a moderate level of reliability for six posture indices (ϕ = 0.51 to 0.72) and a good level of reliability for 26 posture indices out of 32 (ϕ ≥ 0.79). Error attributable to marker placement was negligible for most indices. Limits of agreement and SEM values were larger for shoulder protraction, trunk list, Q angle, cervical lordosis and scoliosis angles. The most reproducible indices were waist angles and knee valgus and varus. Conclusions Posture can be assessed in a global fashion from photographs in persons with idiopathic scoliosis. Despite the good reliability of marker placement, other studies are needed to minimise measurement errors in order to provide a suitable tool for monitoring change in posture over time.

Propagation of Microwaves in the Troposphere with Potential Application to GPS based Navigation and Meteorology with emphasis on Indian region

Global Positioning System (GPS), with its high integrity, continuous availability and reliability, revolutionized the navigation system based on radio ranging. With four or more GPS satellites in view, a GPS receiver can find its location anywhere over the globe with accuracy of few meters. High accuracy - within centimeters, or even millimeters is achievable by correcting the GPS signal with external augmentation system. The use of satellite for critical application like navigation has become a reality through the development of these augmentation systems (like W AAS, SDCM, and EGNOS, etc.) with a primary objective of providing essential integrity information needed for navigation service in their respective regions. Apart from these, many countries have initiated developing space-based regional augmentation systems like GAGAN and IRNSS of India, MSAS and QZSS of Japan, COMPASS of China, etc. In future, these regional systems will operate simultaneously and emerge as a Global Navigation Satellite System or GNSS to support a broad range of activities in the global navigation sector.Among different types of error sources in the GPS precise positioning, the propagation delay due to the atmospheric refraction is a limiting factor on the achievable accuracy using this system. The WADGPS, aimed for accurate positioning over a large area though broadcasts different errors involved in GPS ranging including ionosphere and troposphere errors, due to the large temporal and spatial variations in different atmospheric parameters especially in lower atmosphere (troposphere), the use of these broadcasted tropospheric corrections are not sufficiently accurate. This necessitated the estimation of tropospheric error based on realistic values of tropospheric refractivity. Presently available methodologies for the estimation of tropospheric delay are mostly based on the atmospheric data and GPS measurements from the mid-latitude regions, where the atmospheric conditions are significantly different from that over the tropics. No such attempts were made over the tropics. In a practical approach when the measured atmospheric parameters are not available analytical models evolved using data from mid-latitudes for this purpose alone can be used. The major drawback of these existing models is that it neglects the seasonal variation of the atmospheric parameters at stations near the equator. At tropics the model underestimates the delay in quite a few occasions. In this context, the present study is afirst and major step towards the development of models for tropospheric delay over the Indian region which is a prime requisite for future space based navigation program (GAGAN and IRNSS). Apart from the models based on the measured surface parameters, a region specific model which does not require any measured atmospheric parameter as input, but depends on latitude and day of the year was developed for the tropical region with emphasis on Indian sector.Large variability of atmospheric water vapor content in short spatial and/or temporal scales makes its measurement rather involved and expensive. A local network of GPS receivers is an effective tool for water vapor remote sensing over the land. This recently developed technique proves to be an effective tool for measuring PW. The potential of using GPS to estimate water vapor in the atmosphere at all-weather condition and with high temporal resolution is attempted. This will be useful for retrieving columnar water vapor from ground based GPS data. A good network of GPS could be a major source of water vapor information for Numerical Weather Prediction models and could act as surrogate to the data gap in microwave remote sensing for water vapor over land.

An Error-Localization, Validation and Optimization Tool for Embedded Code Augmentation: an Architecture Oriented Approach

Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.This dissertation contributes to an architecture oriented code validation, error localization and optimization technique assisting the embedded system designer in software debugging, to make it more effective at early detection of software bugs that are otherwise hard to detect, using the static analysis of machine codes. The focus of this work is to develop methods that automatically localize faults as well as optimize the code and thus improve the debugging process as well as quality of the code.Validation is done with the help of rules of inferences formulated for the target processor. The rules govern the occurrence of illegitimate/out of place instructions and code sequences for executing the computational and integrated peripheral functions. The stipulated rules are encoded in propositional logic formulae and their compliance is tested individually in all possible execution paths of the application programs. An incorrect sequence of machine code pattern is identified using slicing techniques on the control flow graph generated from the machine code.An algorithm to assist the compiler to eliminate the redundant bank switching codes and decide on optimum data allocation to banked memory resulting in minimum number of bank switching codes in embedded system software is proposed. A relation matrix and a state transition diagram formed for the active memory bank state transition corresponding to each bank selection instruction is used for the detection of redundant codes. Instances of code redundancy based on the stipulated rules for the target processor are identified.This validation and optimization tool can be integrated to the system development environment. It is a novel approach independent of compiler/assembler, applicable to a wide range of processors once appropriate rules are formulated. Program states are identified mainly with machine code pattern, which drastically reduces the state space creation contributing to an improved state-of-the-art model checking. Though the technique described is general, the implementation is architecture oriented, and hence the feasibility study is conducted on PIC16F87X microcontrollers. The proposed tool will be very useful in steering novices towards correct use of difficult microcontroller features in developing embedded systems.

Environomics - A Financial Estimate of Environmental Pollution Control and Abatement Schemes in Eloor-Edayar Industrial Belt

The present study consists of nine chapters including the introductory chapter. Chapter II makes a brief review of environmental literature and examines various measures adopted at the global level to protect the environment. The environmental problems often transgress national sovereignity and geographical boundaries. Therefore, attempts must be made at the national and international levels to protect the environment, the resources of which are the common property of mankind. The protection of the national environment from the ancient till the present forms the content of Chapter III. These chapters together provide a background to understand the issues analysed in the subsequent chapters. Carefully worked out theoretical framework is a pre-requisite for the successful study of a complex subject. Some of the theoretical issues of ‘environomics’ are examined in Chapter IV. The theoretical issues involved in estimating the costs and benefits of environmental protection constitute the theme of Chapter V. The state of environment in Eloor-Edayar Industrial belt andthe impact analysis of pollution of the area are discussed in Chapter VI and VII respectively. Chapter VIII makes the financial estimate of environmental protection of the project And finally, Chapter IX presents the findings of the study

Fault Tolerant Error Coding and Detection using Reversible Gates

In recent years, reversible logic has emerged as one of the most important approaches for power optimization with its application in low power CMOS, quantum computing and nanotechnology. Low power circuits implemented using reversible logic that provides single error correction – double error detection (SEC-DED) is proposed in this paper. The design is done using a new 4 x 4 reversible gate called ‘HCG’ for implementing hamming error coding and detection circuits. A parity preserving HCG (PPHCG) that preserves the input parity at the output bits is used for achieving fault tolerance for the hamming error coding and detection circuits.

An efficient scheme for the evaluation of coding performance of high speed links incorporating joint error behaviour based on Monte Carlo Method

While channel coding is a standard method of improving a system’s energy efficiency in digital communications, its practice does not extend to high-speed links. Increasing demands in network speeds are placing a large burden on the energy efficiency of high-speed links and render the benefit of channel coding for these systems a timely subject. The low error rates of interest and the presence of residual intersymbol interference (ISI) caused by hardware constraints impede the analysis and simulation of coded high-speed links. Focusing on the residual ISI and combined noise as the dominant error mechanisms, this paper analyses error correlation through concepts of error region, channel signature, and correlation distance. This framework provides a deeper insight into joint error behaviours in high-speed links, extends the range of statistical simulation for coded high-speed links, and provides a case against the use of biased Monte Carlo methods in this setting

A Numerically efficient power optimization scheme for coded OFDM systems in achieving minimum frame error rate

Coded OFDM is a transmission technique that is used in many practical communication systems. In a coded OFDM system, source data are coded, interleaved and multiplexed for transmission over many frequency sub-channels. In a conventional coded OFDM system, the transmission power of each subcarrier is the same regardless of the channel condition. However, some subcarrier can suffer deep fading with multi-paths and the power allocated to the faded subcarrier is likely to be wasted. In this paper, we compute the FER and BER bounds of a coded OFDM system given as convex functions for a given channel coder, inter-leaver and channel response. The power optimization is shown to be a convex optimization problem that can be solved numerically with great efficiency. With the proposed power optimization scheme, near-optimum power allocation for a given coded OFDM system and channel response to minimize FER or BER under a constant transmission power constraint is obtained

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.

Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Digital image analysis as a tool to estimate legume contributions in legume-grass swards

Summary: Productivity and forage quality of legume-grass swards are important factors for successful arable farming in both organic and conventional farming systems. For these objectives the botanical composition of the swards is of particular importance, especially, the content of legumes due to their ability to fix airborne nitrogen. As it can vary considerably within a field, a non-destructive detection method while doing other tasks would facilitate a more targeted sward management and could predict the nitrogen supply of the soil for the subsequent crop. This study was undertaken to explore the potential of digital image analysis (DIA) for a non destructive prediction of legume dry matter (DM) contribution of legume-grass mixtures. For this purpose an experiment was conducted in a greenhouse, comprising a sample size of 64 experimental swards such as pure swards of red clover (Trifolium pratense L.), white clover (Trifolium repens L.) and lucerne (Medicago sativa L.) as well as binary mixtures of each legume with perennial ryegrass (Lolium perenne L.). Growth stages ranged from tillering to heading and the proportion of legumes from 0 to 80 %. Based on digital sward images three steps were considered in order to estimate the legume contribution (% of DM): i) The development of a digital image analysis (DIA) procedure in order to estimate legume coverage (% of area). ii) The description of the relationship between legume coverage (% area) and legume contribution (% of DM) derived from digital analysis of legume coverage related to the green area in a digital image. iii) The estimation of the legume DM contribution with the findings of i) and ii). i) In order to evaluate the most suitable approach for the estimation of legume coverage by means of DIA different tools were tested. Morphological operators such as erode and dilate support the differentiation of objects of different shape by shrinking and dilating objects (Soille, 1999). When applied to digital images of legume-grass mixtures thin grass leaves were removed whereas rounder clover leaves were left. After this process legume leaves were identified by threshold segmentation. The segmentation of greyscale images turned out to be not applicable since the segmentation between legumes and bare soil failed. The advanced procedure comprising morphological operators and HSL colour information could determine bare soil areas in young and open swards very accurately. Also legume specific HSL thresholds allowed for precise estimations of legume coverage across a wide range from 11.8 - 72.4 %. Based on this legume specific DIA procedure estimated legume coverage showed good correlations with the measured values across the whole range of sward ages (R2 0.96, SE 4.7 %). A wide range of form parameters (i.e. size, breadth, rectangularity, and circularity of areas) was tested across all sward types, but none did improve prediction accuracy of legume coverage significantly. ii) Using measured reference data of legume coverage and contribution, in a first approach a common relationship based on all three legumes and sward ages of 35, 49 and 63 days was found with R2 0.90. This relationship was improved by a legume-specific approach of only 49- and 63-d old swards (R2 0.94, 0.96 and 0.97 for red clover, white clover, and lucerne, respectively) since differing structural attributes of the legume species influence the relationship between these two parameters. In a second approach biomass was included in the model in order to allow for different structures of swards of different ages. Hence, a model was developed, providing a close look on the relationship between legume coverage in binary legume-ryegrass communities and the legume contribution: At the same level of legume coverage, legume contribution decreased with increased total biomass. This phenomenon may be caused by more non-leguminous biomass covered by legume leaves at high levels of total biomass. Additionally, values of legume contribution and coverage were transformed to the logit-scale in order to avoid problems with heteroscedasticity and negative predictions. The resulting relationships between the measured legume contribution and the calculated legume contribution indicated a high model accuracy for all legume species (R2 0.93, 0.97, 0.98 with SE 4.81, 3.22, 3.07 % of DM for red clover, white clover, and lucerne swards, respectively). The validation of the model by using digital images collected over field grown swards with biomass ranges considering the scope of the model shows, that the model is able to predict legume contribution for most common legume-grass swards (Frame, 1992; Ledgard and Steele, 1992; Loges, 1998). iii) An advanced procedure for the determination of legume DM contribution by DIA is suggested, which comprises the inclusion of morphological operators and HSL colour information in the analysis of images and which applies an advanced function to predict legume DM contribution from legume coverage by considering total sward biomass. Low residuals between measured and calculated values of legume dry matter contribution were found for the separate legume species (R2 0.90, 0.94, 0.93 with SE 5.89, 4.31, 5.52 % of DM for red clover, white clover, and lucerne swards, respectively). The introduced DIA procedure provides a rapid and precise estimation of legume DM contribution for different legume species across a wide range of sward ages. Further research is needed in order to adapt the procedure to field scale, dealing with differing light effects and potentially higher swards. The integration of total biomass into the model for determining legume contribution does not necessarily reduce its applicability in practice as a combined estimation of total biomass and legume coverage by field spectroscopy (Biewer et al. 2009) and DIA, respectively, may allow for an accurate prediction of the legume contribution in legume-grass mixtures.