Consistency of Deviance-Based M-Estimators

In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-paramet...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1987, Vol.49 (3), p.326-330
Main Authors: Lenth, R. V., Green, P. J.
Format: Article
Language:English
Subjects:
consistency
Consistent estimators
deviance
Estimators
Exact sciences and technology
Linear regression
m estimation
Mathematical vectors
Mathematics
Maximum likelihood estimation
Parametric inference
Probability and statistics
Random variables
robust estimation
robust regression
Sciences and techniques of general use
Statistics
Weighting functions
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Summary:In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many continuous Cramer-Rao-regular families and in related linear or nonlinear regression cases. The conditions fail (and the estimator is inconsistent) in most discrete families.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1987.tb01702.x