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.

scholarly journals On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

scholarly journals The Mixed Liu Estimator in Stochastic Restricted Linear Measurement Error Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jibo Wu
Keyword(s):  
Measurement Error ◽  
Mean Squared Error ◽  
Linear Measurement ◽  
Error Model ◽  
Measurement Error Model ◽  
Error Matrix ◽  
Liu Estimator ◽  
Squared Error ◽  
Mixed Estimator ◽  
Linear Restrictions

Ghapani and Babdi [1] proposed a mixed Liu estimator in linear measurement error model with stochastic linear restrictions. In this article, we propose an alternative mixed Liu estimator in the linear measurement error model with stochastic linear restrictions. The performance of the new mixed Liu estimator over the mixed estimator, Liu estimator, and mixed Liu estimator proposed by Ghapani and Babdi [1] are discussed in the sense of mean squared error matrix. Finally, a simulation study is given to show the performance of these estimators.

Sensor Fault Detection, Diagnosis and Validation - A Survey

2012 ◽  
Vol 229-231 ◽  
pp. 1265-1271 ◽  
Author(s):  
Zhi Gang Yao ◽  
Li Cheng ◽  
Qing Lin Wang
Keyword(s):  
Fault Diagnosis ◽  
Fault Detection ◽  
Principal Components ◽  
Sufficient Conditions ◽  
Data Driven ◽  
Sensor Fault ◽  
Validity Index ◽  
Sensor Fault Detection ◽  
Multiple Sensor ◽  
Necessary And Sufficient

This paper provides an overview and analysis of data-driven sensor fault detection, diagnosis and validation from the application viewpoint. The typical sensor fault detection indices in the literature and the fundamental issues of necessary and sufficient conditions for detectability, reconstructability, identifiability and isolatability are analyzed. The main objective is to study the essential and important algorithms and techniques for single or multiple sensor fault diagnosis and validation. The issues of optimal principal components, sensor validity index, maximized sensitivity, as well as robust sensor fault diagnosis, etc. are discussed. Additional focuses are summarized at the end of the paper for future investigation.

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