scholarly journals Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model

2019 ◽  
Vol 5 (2) ◽  
pp. 18
Author(s):  
Alaa Ahmed Abd Elmegaly
Keyword(s):  
Linear Model ◽  
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.

Estimation of Expression Levels in Spotted Microarrays with Saturated Pixels

2007 ◽  
Vol 6 (1) ◽  
Author(s):  
Chris A Glasbey ◽  
Thorsten Forster ◽  
Peter Ghazal
Keyword(s):  
Gene Expression ◽  
Linear Model ◽  
Principal Components ◽  
Laser Scanning ◽  
Dynamic Range ◽  
Biological Data ◽  
Hyperbolic Model ◽  
Expression Levels ◽  
Biased Estimates ◽  
Gene Expression Levels

Digital images obtained by the laser scanning of spotted microarrays often include saturated pixel values. These arise when the scan settings are sufficiently high and some pixels exceed the limit L=65535 and are instead set to L. Failure to adjust for this censoring leads to biased estimates of gene expression levels. To impute censored values, we propose a linear model based on the principal components of uncensored spots on the same array. This is computationally fast, flexible to adapt to distinctive spot shapes and profiles on different arrays, and is shown to be more effective than the polynomial-hyperbolic model in correcting for the bias. The application to biological data demonstrates the potential for enhancing the dynamic range of detection. Fortran90 subroutines implementing these methods are available at http://www.bioss.ac.uk/~chris.

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