Extended Gauss-Markov Theorem for Nonparametric Mixed-Effects Models

Su-Yun Huang and Henry Horng-Shing Lu

Journal of Multivariate Analysis, 2001, vol. 76, issue 2, 249-266

Abstract: 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.

Keywords: nonparametric; mixed-effects; Gauss-Markov; theorem; best; linear; unbiased; prediction; (BLUP); regularization; minimaxity; normal; equations; nonparametric; regression; wavelet; shrinkage; deconvolution (search for similar items in EconPapers)
Date: 2001
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