Formulas Useful for Linear Regression Analysis and Related Matrix Theory by Simo Puntanen George P. H. Styan & Jarkko Isotalo

Author:Simo Puntanen, George P. H. Styan & Jarkko Isotalo
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

where is a matrix satisfying .

12.15Let be any arbitrary parametric function. Then a necessary condition for is that .

12.16If is linearly sufficient and admissible for an estimable , then is also linearly minimal sufficient for .

13 Best Linear Unbiased Predictor

13.1 : Best linear unbiased predictor. Consider the linear model with new observations:

where is an unobservable random vector containing new observations (observable in future). Above we have , , and

A linear predictor is said to be linear unbiased predictor, , for if for all , i.e., , i.e., . Then is said unbiasedly predictable; the difference is the prediction error. A linear unbiased predictor is the for if

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