arXiv subjects

Graciela Boente

Publications and source records attributed to Graciela Boente.

26 records · Page 2Linked to original sources

arXiv2018

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. 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.

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arXiv2018

The spatial sign covariance operator: Asymptotic results and applications

Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently. One robust alternative to the sample covariance operator is the sample spatial sign covariance operator. In this paper, we study the asymptotic behaviour of the sample spatial sign covariance operator when location is unknown. Among other possible applications of the obtained results, we derive the asymptotic distribution of the principal directions obtained from the sample spatial sign covariance operator and we develop test to detect differences between the scatter operators of two populations. In particular, the test performance is illustrated through a Monte Carlo study for small sample sizes.

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arXiv2018

Robust estimation in single index models when the errors have a unimodal density with unknown nuisance parameter

In this paper, we propose a robust profile estimation method for the parametric and nonparametric components of a single index model when the errors have a strongly unimodal density with unknown nuisance parameter. Under regularity conditions, we derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single index parameter estimators. Under a log--Gamma model, the sensitivity to anomalous observations is studied by means of the empirical influence curve. We also discuss a robust $K-$fold procedure to select the smoothing parameters involved. A numerical study is conducted to evaluate the small sample performance of the robust proposal with that of their classical relatives, both for errors following a log--Gamma model and for contaminated schemes. The numerical experiment shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one.

stat.ME↗

arXiv2016

Testing equality between several populations covariance operators

In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study if this assumption holds before making other inferences. In this paper, we develop a test for comparing covariance operators of several functional data samples. The proposed test is based on the Hilbert--Schmidt norm of the difference between estimated covariance operators. In particular, when dealing with two populations, the tests statistic is just the squared norm of the difference between the two covariance operators estimators. The asymptotic behaviour of the test statistic under the null and under local alternatives is obtained. Since the statistic null asymptotic distribution does not allow to obtain easily its quantiles, a bootstrap procedure to compute the critical values is considered. The performance of the test statistics for small sample sizes is illustrated through a Monte Carlo study.

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arXiv2015

Marginal integration $M-$estimators for additive models

Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal univariate rate. Beyond backfitting, marginal integration is a common procedure to estimate each component. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated and marginal integration. The proposed estimators are consistent and asymptotically normally distributed. A simulation study allows to show the advantage of the proposal over the classical one when outliers are present in the responses, leading to estimators with good robustness and efficiency properties.

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arXiv2015

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.

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arXiv2012

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.

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arXiv2007

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 $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,μ_i)$ with $μ_i=H(η(t_i)+\mathbf{x}_i^{$\mathrm{T}$}β)$, for some known distribution function F and link function H. It is shown that the estimates of $β$ 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.

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