Robust Inference Using the Exponential-Polynomial Divergence

Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Brègman divergence have...

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Bibliographic Details
Published in:Journal of statistical theory and practice Vol. 15; no. 2
Main Authors: Singh, Pushpinder, Mandal, Abhijit, Basu, Ayanendranath
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2021
Subjects:
Celebrating the Centenary of Professor C. R. Rao
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
Robustness
Density power divergence
Brègman divergence
M-estimator
ISSN:1559-8608, 1559-8616
Online Access:Get full text
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Summary:Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Brègman divergence have the attractive property that the empirical formulation of the divergence does not require the use of any nonparametric smoothing technique such as kernel density estimation. The methods based on the density power divergence (DPD) represent the current standard in this area of research. In this paper, we will present a more generalized divergence which subsumes the DPD as a special case, and produces several new options providing better compromises between robustness and efficiency.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-020-00162-z