Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions. Issue 9 (3rd July 2020)

• Record Type: Journal Article
• Authors: da Silva Ferreira, Clécio; Lachos, Víctor H.; Garay, Aldo M.
• Is Part Of: Journal of applied statistics. Volume 47:Issue 9(2020)
• Page Start: 1690
• Page End: 1719
• Publication Date: 2020-07-03
• Subjects: EM algorithm -- heteroscedastic nonlinear regression models -- influence diagnostics -- likelihood ratio test -- skew scale mixtures of normal distributions; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2019.1691158
• Languages: English
• ISSNs: 0266-4763

Abstract

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.