Nonparametric regression function estimation with surrogate data and validation sampling
چکیده
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This paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data. We propose to use Cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously. We further pr
Let (X, Y), (X1, Y1), .•, (X,, Yn ) be independent identically distributed random vectors from R dxR, and let E(I Y 1 p) 1 . We wish to estimate the regression function m(x) = E(Y I X = x) by mn(x), a function of x and (X1 , Y1), .•, (X,, Yn ) . For large classes of kernel estima
to Summary: We prove a law of the iterated logarithm for nonparametric regression function estimators using strong approximations to the two dimensional empirical process. We consider the case of Nadaraya-Watson kernel estimators and of esti-mators based on orthogonal polynomials