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Extended Gauss–Markov Theorem for Nonparametric Mixed-Effects Models

✍ Scribed by Su-Yun Huang; Henry Horng-Shing Lu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
158 KB
Volume
76
Category
Article
ISSN
0047-259X

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✦ Synopsis

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.

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