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Some recent results in the asymptotic theory of statistical estimation. (English) Zbl 0747.62027
Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. II, 1083-1090 (1991).
[For the entire collection see Zbl 0741.00020.]
The author reviews the Hajek-Le Cam asymptotic minimax theorem and indicates how the theorem can be applied to problems recently studied by D. L. Donoho and R. C. Liu [Geometrizing rates of convergence, III. Tech. Rep. 138, Dept. Stat., Berkeley (1990)], by M. G. Low [Local convergence of nonparametric density estimation problems to Gaussian shift experiments on a Hilbert space, Tech. Rep. 225, Dept. Stat., Berkeley (1989)] and by G. K. Golubev and M. Nussbaum [Ann. Stat. 18, No. 2, 758-778 (1990; Zbl 0713.62047)].
62F12 Asymptotic properties of parametric estimators
62B15 Theory of statistical experiments
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation