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

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

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16 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 languageEnglish (US)
Pages (from-to)1208-1217
Number of pages10
JournalStatistics and Probability Letters
Volume81
Issue number8
DOIs
StatePublished - 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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