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

Some Continental European Perspectives on Safeguards in the Case of Deprivation of Liberty in Health and Social Care Settings

This article highlights perspectives and regulations on safeguards in the case of deprivation of liberty of some continental European countries – namely Germany, Switzerland, France, Austria, and Spain. It illustrates the continent’s disparate approaches to the subject, both those founded in history and in the different legal traditions.Continental legislation struggles to cope with the UN Convention on the Rights of Persons with Disabilities. The most recent observations of the Committee on the Rights of Persons with Disabilities in Germany, in May 2015, recommend for example, that Germany “amend legislation to prohibit involuntary placement and promote alternative measures”. Nevertheless, legislation and practice in these countries might provide some different points of view on deprivation of liberty safeguards

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

Robust functional principal components: A projection-pursuit approach

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes.Comment: Published in at http://dx.doi.org/10.1214/11-AOS923 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust estimators in a generalized partly linear regression model under monotony constraints

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log-Gamma regression model. Under regularity conditions, we derive consistency results for the nonparametric function estimators as well as consistency and asymptotic distribution results for the regression parameter estimators. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component. The proposal is illustrated on a real data set.Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rodriguez, Daniela Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Vena, Pablo Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

Robust consistent estimators for ROC curves with covariates

The Receiver Operating Characteristic (ROC) curve is a use-ful tool to measure the classification capability of a continuous variable to assess the accuracy of a medical test that distinguishes between two conditions. Sometimes, covariates related to the diagnostic variable may increase the discriminating power of the ROC curve. Due to the lack of stability of classical ROC curves estimators to outliers, we introduce a procedure to obtain robust estimators in presence of covariates. The considered proposal focusses on a semiparametric approach which robustly fits a location-scale regression model to the diagnostic variable and considers robust adaptive empirical estimators of the regression residuals. The uniform consistency of the proposal is derived under mild assumptions. A Monte Carlo study is carried out to compare the performance of the robust proposed estimators with the classical ones both, in clean and contaminated samples. A real data set is also analysed.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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: González Manteiga, Wenceslao. Universidad de Santiago de Compostela; Españ

Robust bootstrap: an alternative to bootstrapping robust estimators

There is a vast literature on robust estimators, but in some situations it is still not easy to make inferences, such as confidence regions and hypothesis testing. This is mainly due to the following facts. On one hand, in most situations, it is difficult to derive the exact distribution of the estimator. On the other one, even if its asymptotic behaviour is known, in many cases, the convergence to the limiting distribution may be rather slow, so bootstrap methods are preferable since they often give better small sample results. However, resampling methods have several disadvantages including the propagation of anomalous data all along the new samples. In this paper, we discuss the problems arising in the bootstrap when outlying observations are present. We argue that it is preferable to use a robust bootstrap rather than to bootstrap robust estimators and we discuss a robust bootstrap method, the Influence Function Bootstrap denoted IFB. We illustrate the performance of the IFB intervals in the univariate location case and in the logistic regression model. We derive some asymptotic properties of the IFB. Finally, we introduce a generalization of the Influence Function Bootstrap in order to improve the IFB behaviour.Fil: Amado, Conceicao. Universidade de Lisboa; PortugalFil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Pires, Ana M.. Universidade de Lisboa; Portuga