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.

Some general comparative points on Chao’s and Zelterman’s estimators of population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Lifetime of an ocean island volcano feeder zone: constraints from U-Pb dating on coexisting zircon and baddeleyite, and 40Ar/39Ar age determinations, Fuerteventura, Canary Islands

High-precision isotope dilution - thermal ionization mass spectrometry (ID-TIMS) U-Pb zircon and baddeleyite ages from the PX1 vertically layered mafic intrusion Fuerteventura, Canary Islands, indicate initiation of magma crystallization at 22.10 +/- 0.07 Ma. The magmatic activity lasted a minimum of 0.52 Ma. Ar-40/Ar-39 amphibole dating yielded ages from 21.9 +/- 0.6 to 21.8 +/- 0.3, identical within errors to the U-Pb ages, despite the expected 1% theoretical bias between Ar-40/Ar-39 and U-Pb dates. This overlap could result from (i) rapid cooling of the intrusion (i. e., less than the 0.3 to 0.6 Ma 40Ar/39Ar age uncertainties) from closure temperatures (T-c) of zircon (699-988 degrees C) to amphibole (500-600 degrees C); (ii) lead loss affecting the youngest zircons; or (iii) excess argon shifting the plateau ages towards older values. The combination of the Ar-40/Ar-39 and U/Pb datasets implies that the maximum amount of time PX1 intrusion took to cool below amphibole T-c is 0.8 Ma, suggesting PX1 lifetime of 520 000 to 800 000 Ma. Age disparities among coexisting baddeleyite and zircon (22.10 +/- 0.07/0.08/0.15 Ma and 21.58 +/- 0.15/0.16/0.31 Ma) in a gabbro sample from the pluton margin suggest complex genetic relationships between phases. Baddeleyite is found preserved in plagioclase cores and crystallized early from low silica activity magma. Zircon crystallized later in a higher silica activity environment and is found in secondary scapolite and is found close to calcite veins, in secondary scapolite that recrystallised from plagioclase. close to calcite veins. Oxygen isotope delta O-18 values of altered plagioclase are high (+7.7), indicating interaction with fluids derived from host-rock carbonatites. The coexistence of baddeleyite and zircon is ascribed to interaction of the PX1 gabbro with CO2-rich carbonatite-derived fluids released during contact metamorphism.

Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

Islamic mutual funds' financial performance and international investment style: evidence from 20 countries

We pursue the first large-scale investigation of a strongly growing mutual fund type: Islamic funds. Based on an unexplored, survivorship bias-adjusted data set, we analyse the financial performance and investment style of 265 Islamic equity funds from 20 countries. As Islamic funds often have diverse investment regions, we develop a (conditional) three-level Carhart model to simultaneously control for exposure to different national, regional and global equity markets and investment styles. Consistent with recent evidence for conventional funds, we find Islamic funds to display superior learning in more developed Islamic financial markets. While Islamic funds from these markets are competitive to international equity benchmarks, funds from especially Western nations with less Islamic assets tend to significantly underperform. Islamic funds’ investment style is somewhat tilted towards growth stocks. Funds from predominantly Muslim economies also show a clear small cap preference. These results are consistent over time and robust to time varying market exposures and capital market restrictions.

Dissecting the illegal ivory trade: an analysis of ivory seizures data

Reliable evidence of trends in the illegal ivory trade is important for informing decision making for elephants but it is difficult to obtain due to the covert nature of the trade. The Elephant Trade Information System, a global database of reported seizures of illegal ivory, holds the only extensive information on illicit trade available. However inherent biases in seizure data make it difficult to infer trends; countries differ in their ability to make and report seizures and these differences cannot be directly measured. We developed a new modelling framework to provide quantitative evidence on trends in the illegal ivory trade from seizures data. The framework used Bayesian hierarchical latent variable models to reduce bias in seizures data by identifying proxy variables that describe the variability in seizure and reporting rates between countries and over time. Models produced bias-adjusted smoothed estimates of relative trends in illegal ivory activity for raw and worked ivory in three weight classes. Activity is represented by two indicators describing the number of illegal ivory transactions--Transactions Index--and the total weight of illegal ivory transactions--Weights Index--at global, regional or national levels. Globally, activity was found to be rapidly increasing and at its highest level for 16 years, more than doubling from 2007 to 2011 and tripling from 1998 to 2011. Over 70% of the Transactions Index is from shipments of worked ivory weighing less than 10 kg and the rapid increase since 2007 is mainly due to increased consumption in China. Over 70% of the Weights Index is from shipments of raw ivory weighing at least 100 kg mainly moving from Central and East Africa to Southeast and East Asia. The results tie together recent findings on trends in poaching rates, declining populations and consumption and provide detailed evidence to inform international decision making on elephants.

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.

Concordância no diagnóstico radiológico da doença respiratória aguda baixa em crianças

Objetivo: Estudar a concordância no diagnóstico radiológico da doença respiratória aguda baixa (DRAB) em crianças. Métodos: Sessenta radiogramas do tórax de crianças menores de cinco anos foram avaliados, individualmente, por três médicos: um radiologista pediátrico (RP), um pneumologista pediatra (PP) e 1 pediatra experiente no atendimento de sala de emergências (PE). Todas as crianças tinham procurado atendimento por apresentar um quadro agudo de infecção respiratória com aparente participação pulmonar. Os avaliadores desconheciam os diagnósticos originais, mas receberam uma ficha padrão com dados clínicos e laboratoriais dos pacientes no momento da consulta inicial. Variáveis: Agrupadas em cinco categorias: a) qualidade técnica do filme; b) localização da alteração; c) padrões radiográficos; d) outras alterações radiográficas; e) diagnóstico. Análise Estatística: Para estudar a concordância entre as três duplas posíveis de observadores, utilizou-se a estatística de Kappa, aceitándo-se os valores ajustados para viés de prevalência (PABAK). Resultados: Os valores Kappa totais de cada dupla de observadores (RP x PP, RP x PE e PP x PE) foram 0.41, 0.43, e 0.39 respectivamente, o que representa em média, uma concordância interobservadores moderada (0.41). Outras variáveis: “qualidade técnica” teve uma concordância regular (0.30); com “localização”, foi moderada (0.48); com “padrões radiográficos” foi regular (0.29); com “outras alterações radiográficas” foi moderada (0,43); e com “diagnóstico”, regular (0.33). Quanto à concordância global intraobservadores, a mesma foi moderada (0.54), com valores menores dos descritos na literatura. Conclusões: A variabilidade interobservadores é inerente à interpretação dos achados radiológicos, e determinar o diagnóstico exato da DRAB nas crianças tem seus desafíos. Nossos resultados foram similares aos descritos na literatura.

Portfolio efficiency tests with conditioning information using empirical likelihood estimation

We evaluate the use of Generalized Empirical Likelihood (GEL) estimators in portfolios efficiency tests for asset pricing models in the presence of conditional information. Estimators from GEL family presents some optimal statistical properties, such as robustness to misspecification and better properties in finite samples. Unlike GMM, the bias for GEL estimators do not increase as more moment conditions are included, which is expected in conditional efficiency analysis. We found some evidences that estimators from GEL class really performs differently in small samples, where efficiency tests using GEL generate lower estimates compared to tests using the standard approach with GMM. With Monte Carlo experiments we see that GEL has better performance when distortions are present in data, especially under heavy tails and Gaussian shocks.

Reliability of the Knee Examination in Osteoarthritis: Effect of Standardization

Objective. To assess the reliability of physical examination of the osteoarthritic (OA) knee by rheumatologists, and to evaluate the benefits of standardization. Methods. Forty-two physical signs and techniques were evaluated using a 6 X 6 Latin square design. Patients with mild to severe knee OA, based on physical and radiographic signs, were examined in random order prior to and following standardization of techniques. For those signs with dichotomous scales, agreement among the rheumatologists was calculated as the prevalence-adjusted bias-adjusted kappa (PABAK), while for the signs with continuous and ordinal scales, a reliability coefficient (R-c) was calculated using analysis of variance. A PABAK of >0.60 and an Re of >0.80 were considered to indicate adequate reliability. Results. Adequate poststandardization reliability was achieved for 30 of 42 physical signs/techniques (71%). The most highly reliable signs identified by physical examination of the OA knee included alignment by goniometer (R-c = 0.99), bony swelling (R-c = 0.97), general passive crepitus (R-c = 0.96), gait by inspection (PABAK = 0.78), effusion bulge sign (R-c = 0.97), quadriceps atrophy (R. = 0.97), medial tibiofemoral tenderness (R-c = 0.94), lateral tibiofemoral tenderness (R-c = 0.85), patellofemoral tenderness by grind test (R-c = 0.94), and flexion contracture (R-c = 0.95). The standardization process resulted in substantial improvements in reliability for evaluation of a number of physical signs, although for some signs, minimal or no effect of standardization was noted. After standardization, warmth (PABAK = 0.14), medial instability at 30degrees flexion (PABAK = 0.02), and lateral instability at 30degrees flexion (PABAK = 0.34) were the only 3 signs that were highly unreliable. Conclusion. With the exception of physical examinations for instability, a comprehensive knee examination can be performed with adequate reliability. Standardization further improves the reliability for some physical signs and techniques. The application of these findings to future OA studies will contribute to improved outcome assessments in OA.

Impacto del Programa de Alimentación Escolar en el Trabajo Infantil: Una aproximación desde la toma de decisiones familiares

Esta investigación analiza el impacto del Programa de Alimentación Escolar en el trabajo infantil en Colombia a través de varias técnicas de evaluación de impacto que incluyen emparejamiento simple, emparejamiento genético y emparejamiento con reducción de sesgo. En particular, se encuentra que este programa disminuye la probabilidad de que los escolares trabajen alrededor de un 4%. Además, se explora que el trabajo infantil se reduce gracias a que el programa aumenta la seguridad alimentaria, lo que consecuentemente cambia las decisiones de los hogares y anula la carga laboral en los infantes. Son numerosos los avances en primera infancia llevados a cabo por el Estado, sin embargo, estos resultados sirven de base para construir un marco conceptual en el que se deben rescatar y promover las políticas públicas alimentarias en toda la edad escolar.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.