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Millar, P. W.

A general approach to the optimality of minimum distance estimators. (English) Zbl 0584.62041

Trans. Am. Math. Soc. 286, 377-418 (1984).
This paper develops a fairly general approach to the locally asymptotic minimaxity of estimators based on, among others, methods like minimum Hellinger, minimum chi square, minimum M-functions. First an abstract asymptotic minimax result is obtained, which in turn is applied to various practical situations to study the asymptotic minimaxity and asymptotic normality of estimators.
The results obtained unify several studies in literature. Some of the applications include Cramér-von Mises estimation, simple regression and estimators based on spectral functions.
Reviewer: C.Srinivasan

Cited in 1 Review
Cited in 26 Documents

MSC:

62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62G20 Asymptotic properties of nonparametric inference

Keywords:

optimality of minimum distance estimators; separable Hilbert space; asymptotic expansion; quantile function methods; robust estimator; differentiable statistical functional; abstract Wiener space; general approach; locally asymptotic minimaxity of estimators; minimum Hellinger; minimum chi square; minimum M-functions; asymptotic normality; Cramér- von Mises estimation; simple regression; spectral functions
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\textit{P. W. Millar}, Trans. Am. Math. Soc. 286, 377--418 (1984; Zbl 0584.62041)
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