On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors

Jeanne Kowalski; M. T.U. Xin; Roger S. Day; José R. Mendoza-Blanco

doi:10.1093/biomet/84.2.269

On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors

Jeanne Kowalski, M. T.U. Xin, Roger S. Day, José R. Mendoza-Blanco

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

11 Scopus citations

Abstract

Although much work has been done on comparing and contrasting the EM and ECME algorithms, in terms of their rates of convergence, it is not clear what mechanism underlies each and, furthermore, what factors may determine and influence their rates of convergence. In this paper, we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with {-distributed errors. By approaching this computing problem through the use of two data augmentation schemes, as well as variations of these wellknown algorithms, we offer a more composite view on the performance of each.

Original language	English (US)
Pages (from-to)	269-281
Number of pages	13
Journal	Biometrika
Volume	84
Issue number	2
DOIs	https://doi.org/10.1093/biomet/84.2.269
State	Published - 1997
Externally published	Yes

Keywords

ECME
EM
Maximum likelihood
R-distribution
Step-length newton's method

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Agricultural and Biological Sciences (miscellaneous)
Agricultural and Biological Sciences(all)
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1093/biomet/84.2.269

Cite this

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title = "On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors",

abstract = "Although much work has been done on comparing and contrasting the EM and ECME algorithms, in terms of their rates of convergence, it is not clear what mechanism underlies each and, furthermore, what factors may determine and influence their rates of convergence. In this paper, we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with {-distributed errors. By approaching this computing problem through the use of two data augmentation schemes, as well as variations of these wellknown algorithms, we offer a more composite view on the performance of each.",

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note = "Funding Information: Editor, A. P. Dawid, Associate Editor and a referee for their constructive comments, which resulted in an improved manuscript. The research was supported in part by grants from the University of Pittsburgh and the National Institutes of Allergy and Infectious Diseases.",

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AU - Kowalski, Jeanne

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AU - Day, Roger S.

AU - Mendoza-Blanco, José R.

N1 - Funding Information: Editor, A. P. Dawid, Associate Editor and a referee for their constructive comments, which resulted in an improved manuscript. The research was supported in part by grants from the University of Pittsburgh and the National Institutes of Allergy and Infectious Diseases.

PY - 1997

Y1 - 1997

N2 - Although much work has been done on comparing and contrasting the EM and ECME algorithms, in terms of their rates of convergence, it is not clear what mechanism underlies each and, furthermore, what factors may determine and influence their rates of convergence. In this paper, we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with {-distributed errors. By approaching this computing problem through the use of two data augmentation schemes, as well as variations of these wellknown algorithms, we offer a more composite view on the performance of each.

AB - Although much work has been done on comparing and contrasting the EM and ECME algorithms, in terms of their rates of convergence, it is not clear what mechanism underlies each and, furthermore, what factors may determine and influence their rates of convergence. In this paper, we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with {-distributed errors. By approaching this computing problem through the use of two data augmentation schemes, as well as variations of these wellknown algorithms, we offer a more composite view on the performance of each.

KW - ECME

KW - EM

KW - Maximum likelihood

KW - R-distribution

KW - Step-length newton's method

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On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors

Abstract

Keywords

ASJC Scopus subject areas

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