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Minimum-distance and gnostical estimators. (English) Zbl 0677.62024
Summary: This paper is based on the result of Z. Fabian [Information theory, statistical decision functions, random processes, Trans. 10th Prague Conf., Prague 1986, Vol. 1, 305-312 (1988)] who showed that three estimators of P. Kovanic [Probl. Control Inf. Theory 13, 303-319 (1984; Zbl 0583.94008)], derived from non-statistical (gnostical) considerations, are particular cases of $$\alpha$$-estimators which are minimum distance-type estimators proposed by us in Information theory, statistical decision functions, random processes, Trans. 9th Prague Conf., Prague 1982, Vol. A, 103-112 (1983; Zbl 0552.62016). Using known statistical properties of the general $$\alpha$$-estimators, we establish here the corresponding statistical properties of the three gnostical estimators.

##### MSC:
 62F10 Point estimation 62G05 Nonparametric estimation