scholarly journals Universal Domination and Stochastic Domination: $U$-Admissibility and $U$- Inadmissibility of the Least Squares Estimator

1989 ◽  
Vol 17 (1) ◽  
pp. 252-267 ◽  
Author(s):  
Lawrence D. Brown ◽  
Jiunn T. Hwang
Keyword(s):  
Least Squares ◽  
Least Squares Estimator ◽  
Stochastic Domination ◽  
Universal Domination

scholarly journals Consistency for the least squares estimator in nonparametric regression

1996 ◽  
Vol 24 (6) ◽  
pp. 2513-2523 ◽  
Author(s):  
Sara van de Geer ◽  
Marten Wegkamp
Keyword(s):  
Least Squares ◽  
Nonparametric Regression ◽  
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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