On estimation and local influence analysis for measurement errors models under heavy-tailed distributions |
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Authors: | V H Lachos T Angolini C A Abanto-Valle |
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Institution: | 1.Department of Statistics,Campinas State University,Campinas,Brazil;2.Department of Statistics,Federal University of Rio de Janeiro,Rio de Janeiro,Brazil |
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Abstract: | Scale mixtures of normal distributions form a class of symmetric thick-tailed distributions that includes the normal one as
a special case. In this paper we consider local influence analysis for measurement error models (MEM) when the random error
and the unobserved value of the covariates jointly follow scale mixtures of normal distributions, providing an appealing robust
alternative to the usual Gaussian process in measurement error models. In order to avoid difficulties in estimating the parameter
of the mixing variable, we fixed it previously, as recommended by Lange et al. (J Am Stat Assoc 84:881–896, 1989) and Berkane
et al. (Comput Stat Data Anal 18:255–267, 1994). The local influence method is used to assess the robustness aspects of the
parameter estimates under some usual perturbation schemes. However, as the observed log-likelihood associated with this model
involves some integrals, Cook’s well–known approach may be hard to apply to obtain measures of local influence. Instead, we
develop local influence measures following the approach of Zhu and Lee (J R Stat Soc Ser B 63:121–126, 2001), which is based
on the EM algorithm. Results obtained from a real data set are reported, illustrating the usefulness of the proposed methodology,
its relative simplicity, adaptability and practical usage. |
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