Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

Blind source separation using second-order cyclostationary statistics

This paper studies the blind source separation (BSS) problem with the assumption that the source signals are cyclostationary. Identifiability and separability criteria based on second-order cyclostationary statistics (SOCS) alone are derived. The identifiability condition is used to define an appropriate contrast function. An iterative algorithm (ATH2) is derived to minimize this contrast function. This algorithm separates the sources even when they do not have distinct cycle frequencies .

A discourse study of Persian ra

The object marker râ in Persian has been studied extensively in the domain of sentence level syntax. It has been claimed that it functions as a definiteness marker, a specificity marker, and a topicalization marker. This paper focuses on the way it signals identifiability of discourse referents. It is argued that the identifiabilty phenomenon, an aspect of the theory of information flow, can adequately explain the role of this particle as used in actual discourse.

Nonnegative blind source separation by sparse component analysis based on determinant measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Online blind source separation using incremental nonnegative matrix factorization with volume constraint

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Evidential in Persian editorials

Based on the analysis of 267 tokens derived from editorial columns primarily drawn from two Persian newspapers, following on earlier studies by Chafe, Jahani, Lazard, Dahl, Adel, and Dafouze, and inspired by a series of Hyland’s studies on metadiscourse signals, this study has aimed at investigating evidential markers in these columns. In order to come to grips with the types of evidentials, first, we classify them into two major types – inferential and reportative; the reportative evidentials are further classified into four types. The reportative classification is based, in the first place, on whether the source of information comes from an individual or from a government body, hence institutional. The further classifications are based on their identifiability/specificity. Results show that inferential evidentials comprise about 15% of all the tokens. Among the four reportative types, those whose source is individual and identified/specified and those that are institutional and unidentified/unspecified, coded as TYPE 1 and TYPE 4, respectively, have the highest frequency. The results overall show that Persian editorials in these two papers feature a high frequency of attribution of information to identified sources when the source is individual (TYPE 1), but to unidentified sources when the source is institutional (TYPE 4). The results also support other authors (e.g. Lazard) who claim that the imperfective (progressive) aspect marker mi-, which is frequent in Persian, is a marker worthy of consideration in evidentiality.

A (semi-)parametric functional coefficient autoregressive conditional duration model

In this paper, we propose a class of ACD-type models that accommodates overdispersion, intermittent dynamics, multiple regimes, and sign and size asymmetries in financial durations. In particular, our functional coefficient autoregressive conditional duration (FC-ACD) model relies on a smooth-transition autoregressive specification. The motivation lies on the fact that the latter yields a universal approximation if one lets the number of regimes grows without bound. After establishing that the sufficient conditions for strict stationarity do not exclude explosive regimes, we address model identifiability as well as the existence, consistency, and asymptotic normality of the quasi-maximum likelihood (QML) estimator for the FC-ACD model with a fixed number of regimes. In addition, we also discuss how to consistently estimate using a sieve approach a semiparametric variant of the FC-ACD model that takes the number of regimes to infinity. An empirical illustration indicates that our functional coefficient model is flexible enough to model IBM price durations.

Bayesian Analysis for Errors in Variables with Changepoint Models

Changepoint regression models have originally been developed in connection with applications in quality control, where a change from the in-control to the out-of-control state has to be detected based on the avaliable random observations. Up to now various changepoint models have been suggested for differents applications like reliability, econometrics or medicine. In many practical situations the covariate cannot be measured precisely and an alternative model are the errors in variable regression models. In this paper we study the regression model with errors in variables with changepoint from a Bayesian approach. From the simulation study we found that the proposed procedure produces estimates suitable for the changepoint and all other model parameters.

Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum

In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Inhomogenitäten der Leitfähigkeit in der elektrischen Impedanztomographie auf unbeschränkten Gebieten - speziell der Halbebene bzw. dem Halbraum - untersucht. Als Lösungsräume für das direkte Problem, d.h. die Bestimmung des elektrischen Potentials zu vorgegebener Leitfähigkeit und zu vorgegebenem Randstrom, führen wir gewichtete Sobolev-Räume ein. In diesen wird die Existenz von schwachen Lösungen des direkten Problems gezeigt und die Gültigkeit einer Integraldarstellung für die Lösung der Laplace-Gleichung, die man bei homogener Leitfähigkeit erhält, bewiesen. Mittels der Faktorisierungsmethode geben wir eine explizite Charakterisierung von Einschlüssen an, die gegenüber dem Hintergrund eine sprunghaft erhöhte oder erniedrigte Leitfähigkeit haben. Damit ist zugleich für diese Klasse von Leitfähigkeiten die eindeutige Rekonstruierbarkeit der Einschlüsse bei Kenntnis der lokalen Neumann-Dirichlet-Abbildung gezeigt. Die mittels der Faktorisierungsmethode erhaltene Charakterisierung der Einschlüsse haben wir in ein numerisches Verfahren umgesetzt und sowohl im zwei- als auch im dreidimensionalen Fall mit simulierten, teilweise gestörten Daten getestet. Im Gegensatz zu anderen bekannten Rekonstruktionsverfahren benötigt das hier vorgestellte keine Vorabinformation über Anzahl und Form der Einschlüsse und hat als nicht-iteratives Verfahren einen vergleichsweise geringen Rechenaufwand.

Localized potentials in electrical impedance tomography

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L-infinity-conductivities (with positive infima) in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to construct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical impedance tomography.

Structural patterns for document engineering: from an empirical bottom-up analysis to an ontological theory

This thesis aims at investigating a new approach to document analysis based on the idea of structural patterns in XML vocabularies. My work is founded on the belief that authors do naturally converge to a reasonable use of markup languages and that extreme, yet valid instances are rare and limited. Actual documents, therefore, may be used to derive classes of elements (patterns) persisting across documents and distilling the conceptualization of the documents and their components, and may give ground for automatic tools and services that rely on no background information (such as schemas) at all. The central part of my work consists in introducing from the ground up a formal theory of eight structural patterns (with three sub-patterns) that are able to express the logical organization of any XML document, and verifying their identifiability in a number of different vocabularies. This model is characterized by and validated against three main dimensions: terseness (i.e. the ability to represent the structure of a document with a small number of objects and composition rules), coverage (i.e. the ability to capture any possible situation in any document) and expressiveness (i.e. the ability to make explicit the semantics of structures, relations and dependencies). An algorithm for the automatic recognition of structural patterns is then presented, together with an evaluation of the results of a test performed on a set of more than 1100 documents from eight very different vocabularies. This language-independent analysis confirms the ability of patterns to capture and summarize the guidelines used by the authors in their everyday practice. Finally, I present some systems that work directly on the pattern-based representation of documents. The ability of these tools to cover very different situations and contexts confirms the effectiveness of the model.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^