Consistency of D-estimators. (English) Zbl 0599.62038

In ibid. 20, 189-208 (1984; Zbl 0558.62026) the author introduced three classes of D-estimators. In the present paper Fisher’s and strong consistency of these estimators are established. It is shown in particular that the standard D-estimators estimate the parameters from compact spaces strongly consistently for all discrete sample-generating families with the probabilities continuously depending on the parameter. Strong consistency of weak and directed D-estimators of location and scale is established for a wide variety of sample-generating models including irregular ones. Analogous results concerning abstract parametric spaces are presented too.


62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
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