Bayes and best quadratic unbiased estimators for parameters of the covariance matrix in a normal linear model

Optimization ◽  
1974 ◽  
Vol 5 (1) ◽  
pp. 43-67 ◽  
Author(s):  
J. Kleffe ◽  
R. Pincus
Keyword(s):  
Linear Model ◽  
Covariance Matrix ◽  
Unbiased Estimators ◽  
Normal Linear Model

A note on reduction of the number of parameters in linear statistical models

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Statistical Analysis ◽  
Linear Model ◽  
Covariance Matrix ◽  
Statistical Models ◽  
Approximate Model ◽  
Model Matrix ◽  
The Mean ◽  
Linear Statistical Models

AbstractIn certain settings the mean response is modeled by a linear model using a large number of parameters. Sometimes it is desirable to reduce the number of parameters prior to conducting the experiment and prior to the actual statistical analysis. Essentially, it means to formulate a simpler approximate model to the original “ideal” one. The goal is to find conditions (on the model matrix and covariance matrix) under which the reduction does not influence essentially the data fit. Here we try to develop such conditions in regular linear model without and with linear restraints. We emphasize that these conditions are independent of observed data.

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