Statistical inference based on bridge divergences

M -estimators offer simple robust alternatives to the maximum likelihood estimator. The density power divergence (DPD) and the logarithmic density power divergence (LDPD) measures provide two classes of robust M -estimators which contain the MLE as a special case. In each of these families, the robu...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics Vol. 71; no. 3; pp. 627 - 656
Main Authors: Kuchibhotla, Arun Kumar, Mukherjee, Somabha, Basu, Ayanendranath
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.06.2019
Springer Nature B.V
Subjects:
Algorithms
Density
Divergence
Economic models
Economics
Efficiency
Finance
Insurance
Management
Mathematics
Mathematics and Statistics
Maximum likelihood estimators
Monte Carlo simulation
Observational weighting
Parameter estimation
Robustness
Statistical inference
Statistics
Statistics for Business
estimators
Robustness
Divergence
ISSN:0020-3157, 1572-9052
Online Access:Get full text
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Summary:M -estimators offer simple robust alternatives to the maximum likelihood estimator. The density power divergence (DPD) and the logarithmic density power divergence (LDPD) measures provide two classes of robust M -estimators which contain the MLE as a special case. In each of these families, the robustness of the estimator is achieved through a density power down-weighting of outlying observations. Even though the families have proved to be useful in robust inference, the relation and hierarchy between these two families are yet to be fully established. In this paper, we present a generalized family of divergences that provides a smooth bridge between DPD and LDPD measures. This family helps to clarify and settle several longstanding issues in the relation between the important families of DPD and LDPD, apart from being an important tool in different areas of statistical inference in its own right.
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ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-018-0665-x