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Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions

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  • Clécio da Silva Ferreira
  • Víctor H. Lachos
  • Aldo M. Garay

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.

Suggested Citation

  • Clécio da Silva Ferreira & Víctor H. Lachos & Aldo M. Garay, 2020. "Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1690-1719, June.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:9:p:1690-1719
    DOI: 10.1080/02664763.2019.1691158
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    Cited by:

    1. Akram Hoseinzadeh & Mohsen Maleki & Zahra Khodadadi, 2021. "Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 451-467, September.

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