Distributed Weighted Least Squares Estimator Without Prior Distribution Knowledge

2021 ◽  
Author(s):  
Shun Liu ◽  
Zhifei Li ◽  
Weifang Zhang ◽  
Yan Liang
Keyword(s):  
Least Squares ◽  
Prior Distribution ◽  
Weighted Least Squares ◽  
Least Squares Estimator ◽  
Weighted Least Squares Estimator

scholarly journals Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

2020 ◽  
Vol 9 (6) ◽  
pp. 108
Author(s):  
Phil D. Young ◽  
Joshua D. Patrick ◽  
Dean M. Young
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Covariance Structure ◽  
Least Squares Estimator ◽  
Weighted Least Squares Estimator ◽  
Best Linear Unbiased ◽  
Necessary And Sufficient ◽  
Nonnegative Definite

We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

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