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• W2010921398 abstract "Let (X,Y) be a pair of random variables such that X=(X1, …,Xd) ranges over a nondegenerate compact d-dimensional interval C and Y is real-valued. Let the conditional distribution of Y given X have mean θ (X) and satisfy an appropriate moment condition. It is assumed that the distribution of X is absolutely continuous and its density is bounded away from zero and infinity on C. Without loss of generality let C be the unit cube. Consider an estimator of θ having the form of piecewise polynomial of degree kn based on md n cubes of length 1/mn where the coefficients are chosen by the method of least squares based on a random sample of size n from the distribution of (X,Y). Let (kn, mn) be chosen by the FPE procedure. It is shown that the indicated estimator achieves the optimal rate of convergence if θ is p-differentiable and satisfies some further conditions." @default.
• W2010921398 created "2016-06-24" @default.
• W2010921398 creator A5007594787 @default.
• W2010921398 date "1988-01-01" @default.
• W2010921398 modified "2023-09-28" @default.
• W2010921398 title "Optimal rates of convergence for the piecewlse polynomial estimator with the index chosen by the fpe selection rule" @default.
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• W2010921398 doi "https://doi.org/10.1080/03610928808829778" @default.
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