Motivation, existence and equivariance of D-estimators. (English) Zbl 0558.62026

Vajda, Igor

Kybernetika 20, 189-208 (1984).

Author’s introduction: This is the first in a series of papers on D- estimators to be published in Kybernetika. D-estimators are minimizing f- divergence or properly modified f-divergence between theoretical and empirical probability. Suitable specifications of convex functions f yield either new promising estimators, or well-known estimators such as the MLE, or M-estimators, or various minimum distance estimators, motivated so far quite diversely if motivated at all.
The theory of D-estimators can be considered as an alternative to the loss-function-based theory in a systematic development of asymptotic as well as non-asymptotic properties of wide classes of estimators. The present paper is devoted to motivation and examples of D-estimators and to non-asymptotic aspects of the theory such as existence, measurability, continuity, invariance, and equivariance of D-estimators.

Reviewer: P.Ressel

MSC:

62F10	Point estimation
62F12	Asymptotic properties of parametric estimators
62B10	Statistical aspects of information-theoretic topics

Keywords:

maximum likelihood estimators; D-estimators; f-divergence; convex functions; M-estimators; minimum distance estimators; examples; non- asymptotic aspects; existence; measurability; continuity; invariance; equivariance

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