標題: | Extended Gauss-Markov theorem for nonparametric mixed-effects models |
作者: | Huang, SY Lu, HHS 交大名義發表 National Chiao Tung University |
關鍵字: | nonparametric mixed-effects;Gauss-Markov theorem;best linear unbiased prediction (BLUP);regularization;minimaxity;normal equations;nonparametric regression;wavelet shrinkage;deconvolution |
公開日期: | 1-二月-2001 |
摘要: | 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. |
URI: | http://dx.doi.org/10.1006/jmva.2000.1930 http://hdl.handle.net/11536/29859 |
ISSN: | 0047-259X |
DOI: | 10.1006/jmva.2000.1930 |
期刊: | JOURNAL OF MULTIVARIATE ANALYSIS |
Volume: | 76 |
Issue: | 2 |
起始頁: | 249 |
結束頁: | 266 |
顯示於類別: | 期刊論文 |