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Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal
Clécio da Silva Ferreira1, Víctor H Lachos2, Aldo M Garay3
1Department of Statistics, Federal University of Juiz de Fora, Juiz de Fora, Brazil.
Abstract:
The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset.
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