The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model

Yunying Huang and Bing Zheng

Journal of Multivariate Analysis, 2015, vol. 133, issue C, 123-135

Abstract: The necessary and sufficient conditions for the weighted least-squares estimators (WLSEs) of parametric functions K1β1+K2β2+⋯+Kmβm under a multiple partitioned linear model ℳ={y,X1β1+⋯+Xmβm,σ2Σ} to be the sum of the WLSEs of Kiβi under the m small models ℳi={y,Xiβi,σ2Σ},i=1,2,…,m, and for the WLSEs of parametric functions Kiβi under the linear model ℳ to be equal to the WLSEs of parametric function Kiβi under its small model ℳi,i=1,2,…,m are derived. Some statistical properties about the WLSEs of parametric functions are also described.

Keywords: Multiple partitioned linear model; WLSEs; BLUE; Parametric functions; Matrix rank method; Moore–Penrose inverse of matrix (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.jmva.2014.09.009

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