Robust estimates in generalized partially linear models

In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with \mu_i=H(\eta(t_i)+\mathbf{x}_i^{\mathrm{T}}\beta), for some known distribution function F and link function H. It is shown that the estimates of $\beta$ are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.Comment: Published at http://dx.doi.org/10.1214/009053606000000858 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Conditional tests for elliptical symmetry using robust estimators

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions that include elliptical distributions without first moments, we derive the test statistic asymptotic behaviour under the null hypothesis and under special alternatives. Numerical experiments allow to compare the behaviour of the tests based on the sample mean and covariance matrix with that based on robust estimators, under various elliptical distributions and different alternatives. This comparison was done looking not only at the observed level and power but we rather use the size-corrected relative exact power which provides a tool to assess the test statistic skill to detect alternatives. We also provide a numerical comparison with other competing tests.Comment: In press in Communications in Statistics: Theory and Methods, 201

Robust estimation for functional quadratic regression models

Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical estimators. For that reason, the proposal of robust procedures providing reliable estimators in such situations is an important issue. Taking into account that the functional polynomial model is equivalent to a regression model that is a polynomial of the same order in the functional principal component scores of the predictor processes, our proposal combines robust estimators of the principal directions with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Fisher-consistency of the proposed method is derived under mild assumptions. The results of a numerical study show, for finite samples, the benefits of the robust proposal over the one based on sample principal directions and least squares. The usefulness of the proposed approach is also illustrated through the analysis of a real data set which also reveals that when the potential outliers are removed the classical and robust methods behave very similarly.Comment: arXiv admin note: text overlap with arXiv:2006.1615

Robust estimation for functional logistic regression models

This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression, regularization tools are needed to compute estimators for the functional slope. The traditional methods are based on dimension reduction or penalization combined with maximum likelihood or quasi--likelihood techniques and for that reason, they may be affected by misclassified points especially if they are associated to functional covariates with atypical behaviour. The proposal given in this paper adapts some of the best practices used when the covariates are finite--dimensional to provide reliable estimations. Under regularity conditions, consistency of the resulting estimators and rates of convergence for the predictions are derived. A numerical study illustrates the finite sample performance of the proposed method and reveals its stability under different contamination scenarios. A real data example is also presented

Robust inference: a path from the finite to the infinite-dimensional setting

El avance de las nuevas tecnologías ha hecho necesario desarrollar procedimientos estadísticos para estimar funciones o para analizar datos que corresponden a realizaciones de un proceso estocástico. Muchos de los procedimientos utilizados se basan en las mismas ideas que el estimador de mínimos cuadrados en el modelo de regresión lineal siendo por lo tanto muy sensibles a la presencia de un pequeño porcentaje de datos anómalos. En este trabajo, se presentan algunos de los avances obtenidos para definir métodos de inferencia confiables cuando la muestra puede contener datos atípicos tanto para modelos de regresión noparamétrica y semiparamétrica como para el análisis de datos funcionales.The development of new technologies clarified the need of developing new statistical procedures to estimate functions or to analyse data that correspond to realizations of a stochastic process. Many of the standard procedures used are based on the same ideas as the least squares estimator in the linear regression model, being therefore very sensitive to the presence of a small percentage of atypical data. In this paper, we present some of the advances obtained to define reliable inference methods when the sample can contain atypical data both for nonparametric and semiparametric regression models and for functional data analysis.Fil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin

Penalized robust estimators in sparse logistic regression

Sparse covariates are frequent in classification and regression problems where the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are only a small number of nonzero parameters, and for that reason, they are much easier to interpret than dense ones. In this paper, we focus on the logistic regression model and our aim is to address robust and penalized estimation for the regression parameter. We introduce a family of penalized weighted M-type estimators for the logistic regression parameter that are stable against atypical data. We explore different penalization functions including the so-called Sign penalty. We provide a careful analysis of the estimators convergence rates as well as their variable selection capability and asymptotic distribution for fixed and random penalties. A robust cross-validation criterion is also proposed. Through a numerical study, we compare the finite sample performance of the classical and robust penalized estimators, under different contamination scenarios. The analysis of real datasets enables to investigate the stability of the penalized estimators in the presence of outliers.Fil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Chebi, Gonzalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin