Applied Linear Statistical Models.

1975 ◽  
Vol 138 (2) ◽  
pp. 258 ◽  
Author(s):  
V. Barnett ◽  
John Neter ◽  
William Wasserman
Keyword(s):  
Statistical Models ◽  
Linear Statistical Models

scholarly journals All about the ⊥ with its applications in the linear statistical models

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Augustyn Markiewicz ◽  
Simo Puntanen
Keyword(s):  
Statistical Models ◽  
Inner Product ◽  
Real Matrix ◽  
Inner Products ◽  
Column Space ◽  
The Matrix ◽  
Linear Statistical Models ◽  
Extensive List

Abstract For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

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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