Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions
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Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two‑piece distributions Akram Hoseinzadeh1 · Mohsen Maleki2 · Zahra Khodadadi1 Received: 9 February 2020 / Accepted: 12 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two–piece distributions based on the scale mixtures of normal (TP– SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP–SMN is a rich class of distributions that covers symmetric and asymmetric as well as heavy-tailed distributions. Using the suitable hierarchical representation of the family, the researchers first derived an EM–type algorithm for iteratively computing maximum likelihood (ML) estimates of the parameters. Then, in order to examine the performance of the proposed models and methods, some simulation studies were presented to show the robust aspect of this flexible class against outlying and also atypical data. As the last step, a natural real dataset was fitted under the proposed HNLR models. Keywords ECME algorithm · Heteroscedastic nonlinear regression model · Two– piece scale mixtures of normal distributions
1 Introduction Although using the nonlinear regression (NLR) model based on the normal distribution to statistical model creates some problems in the presence of asymmetrical and atypical datasets, the symmetrical nonlinear regression (NLR) models are useful statistical tools to describe and model the phenomenological datasets in some scientific fields (see, e.g., Cysneiros and Vanegas 2008; Vanegas and Cysneiros 2010; Cordeiro et al. 2010, Pan et al. 2019). Also, in regression analysis, not only the assumption of the equality of the variances of the error terms is common in * Mohsen Maleki [email protected] 1
Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
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Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746‑73441, Iran
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application but also its violation can have adverse consequences for the efficiency of estimators (Cysneiros et al. 2010). Xie et al. (2009a) and Xie et al. (2009b) developed score test statistics for testing homogeneity of the NLR model in the absence of atypical data. The novel class of HNLR models (Cysneiros et al. 2010; Ferreira et al. 2020) provided a useful generalization of the NLR models of Cysneiros et al. (2008), to solve the mentioned issue. Also existence of the asymmetrical behaviors of data and outliers, are the other problematic issues on the study of the ordinary NLR model. Recently, many researchers have used the well-known distributional forms in the structure of statistical models to solve the some mentioned issues, see, e.g., Contreras-Reyes and Arellano-Valle (2013), Ferreira et al. (2015), Contreras-Reyes
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