Statist. Efroimovich, S., and Pinsker, M. (1982). Estimation of square-integrable [spectral] density based on a sequence of observations. Problems of Information Transmission, 182--196.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....concept used in the definition of n widths in approximation theory in Section 2. The construction of minimax non parametric regression estimators for different sets F is a hard problem. Presently, it has only solved asymptotically (for large samples) for some special cases (see, for instance, (Efroimovich and Pinsker, 1982), Efroimovich and Pinsker, 1983) Efroimovich and Pinsker, 1984) However, letting aN decrease as fast as possible so that the minimax risk still remains bounded yields a notion of a best achievable convergence rate, similar to that of parametric estimation. More precisely, we state the ....

....e is known. Set V m;N = k b f m;N Gamma fk 2 2 . Then for the estimate (56) 57) and (62) it holds that VmN ;N minm V m;N 1 a.e. as N 1 : Another classical adaptation approach is closely related to the problem of filtering of a Gaussian stationary process. The technique developed in (Efroimovich and Pinsker, 1982), 10 In fact, a similar result holds for the spline or piecewise polynomial ones. Efroimovich and Pinsker, 1984) for the projection estimates is often referred to as EfromovichPinsker filter. To understand the idea of the method let us consider the estimates b c j , j = 1; N of the ....

Efroimovich, S. and Pinsker, M. (1982). Estimation of square-integrable spectral density based on a sequence of observations. Problems of Information Transmission (in Russian), pp.

....estimator and the value min b fN sup f2F R aN ( b f N ; f) the minimax risk on F . The construction of minimax nonparametric regression estimators for different sets F is a hard problem. Today, it is only solved asymptotically (for large samples) for some special cases (see, for instance, [34], 35] 36] However, letting aN decrease as fast as possible so that the minimax risk still remains bounded yields a notion of a best achievable convergence rate, similar to that of parametric estimation. More precisely, we state the following definition : Definition 1 (lower rate and minimax ....

S. Efroimovich and M. Pinsker, Estimation of square-integrable spectral density based on a sequence of observations, Problems of Information Transmission (in Russian), pp. 182-196 (1982).

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Statist. Efroimovich, S., and Pinsker, M. (1982). Estimation of square-integrable [spectral] density based on a sequence of observations. Problems of Information Transmission, 182--196.

No context found.

Statist. Efroimovich, S., and Pinsker, M. (1982). Estimation of square-integrable [spectral] density based on a sequence of observations. Problems of Information Transmission, 182--196.

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