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Extended Gauss-Markov theorem for nonparametric mixed-effects models
(2001-02-01)
Huang, SY
;
Lu, HHS
;
交大名義發表
;
National Chiao Tung University
The Gauss-Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss-Markov theorem to include nonparametric mixed-effects models. The extended Gauss-Markov estimation (or prediction) is shown to be equivalent to a regularization method and its minimaxity is addressed. The resulting Gauss-Markov estimation serves as an oracle to guide the exploration for effective nonlinear estimators adaptively. Various examples are discussed. Particularly, the wavelet nonparametric regression example and its connection with a Sobolev regularization is presented. (C) 2001 Academic Press.