Motivation, existence and equivariance of D-estimators

This is the first in a series of papers on O-estimators to be published in Kybernetika. D-estimators are minimizing/-divergence or properly modified/-divergence between theoretical and empirical probability. Suitable specifications of convex functions/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 £>-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 Destimators.