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Minimax linear estimation in a white noise problem. (English) Zbl 0879.62033
Summary: Linear estimation of \(f(x)\) at a point in a white noise model is considered. The exact linear minimax estimator of \(f(0)\) is found for the family of \(f(x)\) in which \(f'(x)\) is \(\text{Lip}(M)\). The resulting estimator is then used to verify a conjecture of J. Sacks and D. Ylvisaker [ibid. 9, 334-346, (1981; Zbl 0458.62031)] concerning the near optimality of the Epanechnikov kernel [V. A. Epanechnikov, Teor. Veroyatn. Primen. 14, 156-162 (1969; Zbl 0175.17101)].

MSC:
62G07 Density estimation
62M05 Markov processes: estimation; hidden Markov models
62G20 Asymptotic properties of nonparametric inference
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[13] PHILADELPHIA, PENNSy LVANIA 19104 E-MAIL: lzhao@stat.wharton.upenn.edu
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