Combining principal component and robust ridge estimators in linear regression model with multicollinearity and outlier

2022 ◽  
Author(s):  
Kingsley Chinedu Arum ◽  
Fidelis Ifeanyi Ugwuowo
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Principal Component

scholarly journals PRINCIPAL COMPONENTS TO OVERCOME MULTICOLLINEARITY PROBLEM

2019 ◽  
Vol 4 (1) ◽  
pp. 79-91 ◽  
Author(s):  
Abubakari S. Gwelo
Keyword(s):  
Principal Component Analysis ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Combination ◽  
Principal Components ◽  
Linear Regression Model ◽  
Principal Component ◽  
Component Analysis ◽  
Ordinary Least Squares ◽  
The Impact

The impact of ignoring collinearity among predictors is well documented in a statistical literature. An attempt has been made in this study to document application of Principal components as remedial solution to this problem. Using a sample of six hundred participants, linear regression model was fitted and collinearity between predictors was detected using Variance Inflation Factor (VIF). After confirming the existence of high relationship between independent variables, the principal components was utilized to find the possible linear combination of variables that can produce large variance without much loss of information. Thus, the set of correlated variables were reduced into new minimum number of variables which are independent on each other but contained linear combination of the related variables. In order to check the presence of relationship between predictors, dependent variables were regressed on these five principal components. The results show that VIF values for each predictor ranged from 1 to 3 which indicates that multicollinearity problem was eliminated. Finally another linear regression model was fitted using Principal components as predictors. The assessment of relationship between predictors indicated that no any symptoms of multicollinearity were observed. The study revealed that principal component analysis is one of the appropriate methods of solving the collinearity among variables. Therefore this technique produces better estimation and prediction than ordinary least squares when predictors are related. The study concludes that principal component analysis is appropriate method of solving this matter.

Statistical Inference and Application for Partially Linear Models

2015 ◽  
Vol 733 ◽  
pp. 910-913
Author(s):  
Jing Zhang ◽  
Hong Xia Guo
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Model ◽  
Linear Regression Model ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Principal Component ◽  
Partial Linear Model ◽  
Partially Linear Regression Model ◽  
Partially Linear

As partially linear regression model contains parameters part and the nonparametric part, it is better than the linear model. Partially linear regression model is more freedom, flexible, and can seize the characteristics of data. This passage first reduces the dimension of expenditure index data using principal component analysis. Then based on the dimension-reduced data, a partial linear model is established to forecast expenditure on army. The results show a great advantage over those by stepwise linear regression analysis.

scholarly journals Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yalian Li ◽  
Hu Yang
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Principal Component ◽  
Monte Carlo Simulation Study ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Almost Unbiased

This paper is concerned with the parameter estimator in linear regression model. To overcome the multicollinearity problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. 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 Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

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