Two Stochastic Restricted Principal Components Regression Estimator in Linear Regression

2013 ◽  
Vol 42 (20) ◽  
pp. 3793-3804 ◽  
Author(s):  
Jibo Wu ◽  
Hu Yang
Keyword(s):  
Linear Regression ◽  
Principal Components ◽  
Regression Estimator ◽  
Principal Components Regression

scholarly journals A Stochastic Restricted Principal Components Regression Estimator in the Linear Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Daojiang He ◽  
Yan Wu
Keyword(s):  
Linear Model ◽  
Principal Components ◽  
Mean Squared Error ◽  
Sufficient Conditions ◽  
Monte Carlo Study ◽  
Regression Estimator ◽  
Principal Components Regression ◽  
Error Matrix ◽  
Necessary And Sufficient ◽  
Linear Restrictions

We propose a new estimator to combat the multicollinearity in the linear model when there are stochastic linear restrictions on the regression coefficients. The new estimator is constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator, which is called the stochastic restricted principal components (SRPC) regression estimator. Necessary and sufficient conditions for the superiority of the SRPC estimator over the OME and the PCR estimator are derived in the sense of the mean squared error matrix criterion. Finally, we give a numerical example and a Monte Carlo study to illustrate the performance of the proposed estimator.

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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