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收集所有交通大學研究人員與學生個人或團體所發表之各項學術著作，涵蓋期刊論文、教師專書、學位論文等項。;;Collections of Publications of NCTU Researchers and Students Like Journal Papers and Thesis.

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Subject: search.filters.subject.best linear unbiased prediction (BLUP)

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    Bayesian wavelet shrinkage for nonparametric mixed-effects models
    (2000-10-01)
    Huang, SY
    ;
    Lu, HHS
    ;
    統計學研究所
    ;
    Institute of Statistics
    The main purpose of this article is to study the wavelet shrinkage method from a Bayesian viewpoint. Nonparametric mixed-effects models are proposed and used for interpretation of the Bayesian structure. Bayes and empirical Bayes estimation are discussed. The latter is shown to have the Gauss-Markov type optimality (i.e., BLUP), to be equivalent to a method of regularization estimator (MORE), and to be minimax in a certain class. Characterization of prior and posterior regularity is discussed. The smoothness of posterior estimators is controlled via prior parameters. Computational issues including the use of generalized cross validation are discussed, and examples are presented.
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    Item type:Item,
    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.