Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression

1990 ◽  
Vol 52 (2) ◽  
pp. 237-258 ◽  
Author(s):  
M. Stone ◽  
R. J. Brooks
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Principal Components ◽  
Ordinary Least Squares ◽  
Principal Components Regression ◽  
Continuum Regression

scholarly journals Comparison of Some Estimators under the Pitman’s Closeness Criterion in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jibo Wu
Keyword(s):  
Least Squares ◽  
Principal Components ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Regression Estimator ◽  
Principal Components Regression ◽  
Ridge Estimator ◽  
Error Matrix ◽  
Ordinary Least Squares Estimator

Batah et al. (2009) combined the unbiased ridge estimator and principal components regression estimator and introduced the modifiedr-kclass estimator. They also showed that the modifiedr-kclass estimator is superior to the ordinary least squares estimator and principal components regression estimator in the mean squared error matrix. In this paper, firstly, we will give a new method to obtain the modifiedr-kclass estimator; secondly, we will discuss its properties in some detail, comparing the modifiedr-kclass estimator to the ordinary least squares estimator and principal components regression estimator under the Pitman closeness criterion. A numerical example and a simulation study are given to illustrate our findings.

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