Robust statistical inference based on the C-divergence family

This paper describes a family of divergences, named herein as the C -divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other diverg...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics Vol. 71; no. 5; pp. 1289 - 1322
Main Authors: Maji, Avijit, Ghosh, Abhik, Basu, Ayanendranath, Pardo, Leandro
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.10.2019
Springer Nature B.V
Subjects:
Computer simulation
Divergence
Economic models
Economics
Estimators
Finance
Hypothesis testing
Influence functions
Insurance
Management
Mathematics
Mathematics and Statistics
Statistical inference
Statistics
Statistics for Business
Generalized power divergence
Divergence
Density power divergence
Power divergence
ISSN:0020-3157, 1572-9052
Online Access:Get full text
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Summary:This paper describes a family of divergences, named herein as the C -divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics of the corresponding minimum distance estimator including its asymptotic distribution under both discrete and continuous models; we also explore the use of the C -divergence family in parametric tests of hypothesis. We study the influence function of these minimum distance estimators, in both the first and second order, and indicate the possible limitations of the first-order influence function in this case. We also briefly study the breakdown results of the corresponding estimators. Some simulation results and real data examples demonstrate the small sample efficiency and robustness properties of the estimators.
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ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-018-0678-5