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.

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576

Single Frame Image Super Resolution Using Learned Directionlets

In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture directional features and to extract edge information along different directions of a set of available high resolution images .This information is used as the training set for super resolving a low resolution input image and the Directionlet coefficients at finer scales of its high-resolution image are learned locally from this training set and the inverse Directionlet transform recovers the super-resolved high resolution image. The simulation results showed that the proposed approach outperforms standard interpolation techniques like Cubic spline interpolation as well as standard Wavelet-based learning, both visually and in terms of the mean squared error (mse) values. This method gives good result with aliased images also.

The spatial prediction of soil mineral N and potentially available N using elevation

The precision farmer wants to manage the variation in soil nutrient status continuously, which requires reliable predictions at places between sampling sites. Ordinary kriging can be used for prediction if the data are spatially dependent and there is a suitable variogram model. However, even if data are spatially correlated, there are often few soil sampling sites in relation to the area to be managed. If intensive ancillary data are available and these are coregionalized with the sparse soil data, they could be used to increase the accuracy of predictions of the soil properties by methods such as cokriging, kriging with external drift and regression kriging. This paper compares the accuracy of predictions of the plant available N properties (mineral N and potentially available N) for two arable fields in Bedfordshire, United Kingdom, from ordinary kriging, cokriging, kriging with external drift and regression kriging. For the last three, intensive elevation data were used with the soil data. The mean squared errors of prediction from these methods of kriging were determined at validation sites where the values were known. Kriging with external drift resulted in the smallest mean squared error for two of the three properties examined, and cokriging for the other. The results suggest that the use of intensive ancillary data can increase the accuracy of predictions of soil properties in arable fields provided that the variables are related spatially. (c) 2005 Elsevier B.V. All rights reserved.

Estimators in capture–recapture studies with two sources

This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Improved channel estimation in TDMA by reproduction with applications in GSM/GPRS under co-channel interference

Finding an estimate of the channel impulse response (CIR) by correlating a received known (training) sequence with the sent training sequence is commonplace. Where required, it is also common to truncate the longer correlation to a sub-set of correlation coefficients by finding the set of N sequential correlation coefficients with the maximum power. This paper presents a new approach to selecting the optimal set of N CIR coefficients from the correlation rather than relying on power. The algorithm reconstructs a set of predicted symbols using the training sequence and various sub-sets of the correlation to find the sub-set that results in the minimum mean squared error between the actual received symbols and the reconstructed symbols. The application of the algorithm is presented in the context of the TDMA based GSM/GPRS system to demonstrate an improvement in the system performance with the new algorithm and the results are presented in the paper. However, the application lends itself to any training sequence based communication system often found within wireless consumer electronic device(1).

The full-spectrum correlated-k method for longwave atmospheric radiative transfer using an effective Planck function

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

The full-spectrum correlated k method for longwave atmospheric radiative transfer: treatment of gaseous overlap

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models, and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas, and performing a pseudo-monochromatic radiation calculation for each point. In this paper it is first argued that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer pseudo-monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K d−1 due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K d−1 can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K d−1 for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Convergence analysis of chip- and fractionally spaced LMS adaptive multiuser CDMA detectors

This paper analyzes the convergence behavior of the least mean square (LMS) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited. The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of the transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, a initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the a noise subspace.

Volatility forecasting for risk management

Recent research has suggested that forecast evaluation on the basis of standard statistical loss functions could prefer models which are sub-optimal when used in a practical setting. This paper explores a number of statistical models for predicting the daily volatility of several key UK financial time series. The out-of-sample forecasting performance of various linear and GARCH-type models of volatility are compared with forecasts derived from a multivariate approach. The forecasts are evaluated using traditional metrics, such as mean squared error, and also by how adequately they perform in a modern risk management setting. We find that the relative accuracies of the various methods are highly sensitive to the measure used to evaluate them. Such results have implications for any econometric time series forecasts which are subsequently employed in financial decisionmaking.

Cloud droplet size and liquid water path retrievals from zenith radiance measurements: examples from the Atmospheric Radiation Measurement Program and the Aerosol Robotic Network

The ground-based Atmospheric Radiation Measurement Program (ARM) and NASA Aerosol Robotic Net- work (AERONET) routinely monitor clouds using zenith ra- diances at visible and near-infrared wavelengths. Using the transmittance calculated from such measurements, we have developed a new retrieval method for cloud effective droplet size and conducted extensive tests for non-precipitating liquid water clouds. The underlying principle is to combine a liquid-water-absorbing wavelength (i.e., 1640 nm) with a non-water-absorbing wavelength for acquiring information on cloud droplet size and optical depth. For simulated stratocumulus clouds with liquid water path less than 300 g m−2 and horizontal resolution of 201 m, the retrieval method underestimates the mean effective radius by 0.8μm, with a root-mean-squared error of 1.7 μm and a relative deviation of 13%. For actual observations with a liquid water path less than 450 g m−2 at the ARM Oklahoma site during 2007– 2008, our 1.5-min-averaged retrievals are generally larger by around 1 μm than those from combined ground-based cloud radar and microwave radiometer at a 5-min temporal resolution. We also compared our retrievals to those from combined shortwave flux and microwave observations for relatively homogeneous clouds, showing that the bias between these two retrieval sets is negligible, but the error of 2.6 μm and the relative deviation of 22 % are larger than those found in our simulation case. Finally, the transmittance-based cloud effective droplet radii agree to better than 11 % with satellite observations and have a negative bias of 1 μm. Overall, the retrieval method provides reasonable cloud effective radius estimates, which can enhance the cloud products of both ARM and AERONET.