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On estimation in LAMN families when there are nuisance parameters present. (English) Zbl 0664.62035

The author studies the problem of estimation in locally asymptotically mixing normal families when nuisance parameters are present. A lower bound for the local asymptotic risk of an estimate of the parameter of interest is obtained and a sufficient condition for an estimate to attain the lower bound is given. A necessary condition for adaptive estimation is also derived. Some illustrative examples are given.
The present results generalize those of J. M. Begun, W. J. Hall, W. Huang and J. A. Wellner [Ann. Stat. 11, 432-452 (1983; Zbl 0526.62045)] and P. Jeganathan [Sankhya, Ser. A 45, 66- 87 (1983; Zbl 0574.62035)].
Reviewer: M.Huškova

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62F12 Asymptotic properties of parametric estimators
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