Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

Victor H. Lachos; Dipankar Bandyopadhyay; Aldo M. Garay

doi:10.1016/j.spl.2011.03.019

Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

Victor H. Lachos, Dipankar Bandyopadhyay, Aldo M. Garay

Biostatistics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.

Original language	English (US)
Pages (from-to)	1208-1217
Number of pages	10
Journal	Statistics and Probability Letters
Volume	81
Issue number	8
DOIs	https://doi.org/10.1016/j.spl.2011.03.019
State	Published - Aug 2011

Bibliographical note

Funding Information:
The research of V.H. Lachos was supported in part by grants from FAPESP-Brazil ( 2010/012465 ) and CNPq-Brazil ( 201384/2008-6 ). D. Bandyopadhyay acknowledges support from NIH/NCRR grant P20 RR017696-06 . The authors thank an anonymous referee whose constructive comments led to a substantially improved version of this manuscript.

Keywords

EM algorithm
Homogeneity
Nonlinear regression models
Scale mixtures
Skew-normal

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abstract = "An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.",

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AU - Garay, Aldo M.

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AB - An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.

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KW - Homogeneity

KW - Nonlinear regression models

KW - Scale mixtures

KW - Skew-normal

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Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

Abstract

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Keywords

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