On bayesian robustness: an asymptotic approach

This paper presents a new asymptotic approach to study the robustness of Bayesian inference to changes on the prior distribution. We study the robustness of the posterior density score function when the uncertainty about the prior distribution has been restated as a problem of uncertainty about the model parametrization. Classical robustness tools, such as the influence function and the maximum bias function, are defined for uniparametric models and calculated for the location case. Possible extensions to other models are also briefly discussed

A simple diagnostic tool for local prior sensitivity

This paper presents a simple diagnostic tool to assess the sensitivity of the posterior mode in the presence of an infinitesimal contamination in the prior distribution. The proposed diagnostic measure is easy to compute and can be used as a first step in judging the robustness of the bayesian inference. The procedure is illustrated in the estimation of the mean of a normal distribution. Some extensions of this diagnostic measure to the multivariate case and credibility intervals are briefly discussed

A multivariate Kolmogorov-Smornov test of goodnes of fit

This paper presents a distribution free multivariate Kolmogorov-Smirnov goodıness of fit test. The test uses an statistic which is built using Rosenblatt's transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulationı study

On the maxbias curve of residual admissible robust regression estimates

The robustness properties of a regression estimate are throughly described by its maxbias curve. However, this function is difficult to compute, especially when the regressors are not elliptically distributed. In this paper, we propose a general method for computing maxbias curves, valid for a large number of robust regression estimates, namely, those estimates defined by residual admissible functionals. Our results are also useful to compute maxbias curves when the regressors are not elliptically distributed. \Ve provide several examples of application of the method which include S-, T-, and signed R-estimates. MM-estimates are also studied under a related, although slightly different, approach

Ranking Edges and Model Selection in High-Dimensional Graphs

In this article we present an approach to rank edges in a network modeled through a Gaussian Graphical Model. We obtain a path of precision matrices such that, in each step of the procedure, an edge is added. We also guarantee that the matrices along the path are symmetric and positive definite. To select the edges, we estimate the covariates that have the largest absolute correlation with a node conditional to the set of edges estimated in previous iterations. Simulation studies show that the procedure is able to detect true edges until the sparsity level of the population network is recovered. Moreover, it can add efficiently true edges in the first iterations avoiding to enter false ones. We show that the top-rank edges are associated with the largest partial correlated variables. Finally, we compare the graph recovery performance with that of Glasso under different settings.The research of Ginette Lafit and Francisco J. Nogales is supported by the Spanish Government through project MTM2013-44902-

Global robustness of location and dispersion estimates

We analyze the global robustness of location and dispersion estimates using the concept of relative explosion rate. The merits of several dispersion estimates are compared when the dispersion parameter itself is of main interest and also when they are auxiliary estimates needed to define scale equivariant location M-estimates. We have also compared location M-estimates and found that the choice of score function (its shape) is of secondary importance in comparison with the choice of the tuning constant and the auxiliary dispersion estimate. Finally, we use the explosion rate to assess the combined effect of the tuning constant and auxiliary dispersion estimate on the global robustness properties of location M-estimates.Sin financiación0.298 JCR (1999) Q3, 46/64 Statistic & probabilityUE

A multivariate Kolmogorov-Smirnov test of goodness of fit

This paper presents a distribution-free multivariate Kolmogorov-Smirnov goodness-of-fit test. The test uses a statistic which is built using Rosenblatt's transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulation study.Bonferroni inequality Empirical distribution function Kolmogorov-Smirnov statistics Rosenblatt's transformation

Bandwidth choice for robust nonparametric scale function estimation

We introduce and compare several robust procedures for bandwidth selection when estimating the variance function. These bandwidth selectors are to be used in combination with the robust scale estimates introduced by Boente et al. (2010a). We consider two different robust cross--validation strategies combined with two ways for measuring the cross--validation prediction error. The different proposals are compared with non robust alternatives using Monte Carlo simulation. We also derive some asymptotic results to investigate the large sample performance of the corresponding robust data--driven scale estimators.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"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Ruiz, Marcelo. Universidad Nacional de Rio Cuarto; ArgentinaFil: Zamar, Rubén. University Of British Columbia; Canad