Computational Statistics & Data Analysis 52 (2007) 1132 – 1142 www.elsevier.com/locate/csda Local influence assessment in heteroscedastic measurement error models Mário de Castro a , ∗ , Manuel Galea-Rojas b , Heleno Bolfarine c a Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos-SP, Brazil b Universidad de Valparaíso, Casilla 5030, Valparaíso, Chile c Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, Ag. Cidade de São Paulo, 05311-970, São Paulo-SP, Brazil Available online 17 May 2007 Abstract Functional heteroscedastic measurement error models are investigated aiming to assess the effects of perturbations of data on some inferential procedures. This goal is accomplished by resorting to methods of local influence. The techniques provide to the practitioner a valuable tool that enables to identify potential influential elements and to quantify the effects of perturbations in these elements on results of interest. An illustrative example with a real data set is also reported. © 2007 Elsevier B.V. All rights reserved. Keywords: Regression analysis; Measurement error models; Maximum likelihood; Local influence 1. Introduction Heteroscedastic measurement error models have received attention in the literature (see Fuller, 1987; Ripley and Thompson, 1987; Riu and Rius, 1996; Galea-Rojas et al., 2003; de Castro et al., 2004; Kukush and Van Huffel, 2004; de Castro et al., 2006a; Markovsky et al., 2006, among others). These works concentrate on parameter estimation and hypothesis testing. de Castro et al. (2006b) develop a local influence study, but they cover solely test statistics in a simple model (one response). The chief aim of the present paper is the assessment of effects of minor perturbations of data on inferential results. To accomplish this goal we resort to methods of local influence. The roots of these methods are in the assessment of the individual impact of observations in a global sense, that is, an observation is either included or deleted in the analysis. There are three major points. First, meaningful perturbation schemes should be choosen in advance. Second, a selection of which particular aspects (for instance, parameter estimates) will be tracked under the perturbations. At last, an objective criterion to quantify the effects of perturbations. The remaining of the paper is organized as follows. Besides the formulation of the working model, for the sake of completeness, maximum likelihood (ML) parameter estimation and hypothesis testing (as in de Castro et al., 2004) are sketched. Next, we provide a short account of the local influence assessment methodologies proposed by Cook (1986), ∗ Corresponding author. Tel.: +55 16 3373 9567; fax: +55 16 3373 9751. E-mail address: mcastro@icmc.usp.br (M. de Castro). 0167-9473/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.csda.2007.05.012