Best Quadratic Unbiased Prediction in a General Linear Model with Stochastic Regression Coefficients |
| |
Authors: | Xu-Qing Liu Yan-Dong Wu Jian-Ying Rong |
| |
Affiliation: | 1. Faculty of Mathematics and Physics , Huaiyin Institute of Technology , Huai'an, P.R. China liuxuqing688@gmail.com;3. Faculty of Mathematics and Physics , Huaiyin Institute of Technology , Huai'an, P.R. China;4. Department of Foundation Courses , Huai'an College of Information Technology , Huai'an, P.R. China |
| |
Abstract: | In this article, we discuss on how to predict a combined quadratic parametric function of the form β′ H β + hσ2 in a general linear model with stochastic regression coefficients denoted by y = X β + e . Firstly, the quadratic predictability of β′ H β + hσ2 is investigated to obtain a quadratic unbiased predictor (QUP) via a general method of structuring an unbiased estimator. This QUP is also optimal in some situations and therefore we hope it will be a fine predictor. To show this idea, we apply the Lagrange multipliers method to this problem and finally reach the expected conclusion through permutation matrix techniques. |
| |
Keywords: | Best quadratic unbiased predictor Permutation matrix Quadratic predictability Stochastic regression coefficient |
|
|