Nonparametric Principal Components Regression
Erniel B. Barrios1, Jennifer D. Umali2
1School of Statistics, University of the Philippines Diliman, Quezon City, Philippines; 2School of Statistics, University of the Philippines Diliman, Quezon City, Philippines

Modeling of high dimensional data is often impaired with specification bias and multicollinearity. Principal components regression can resolve multicollinearity but specification bias remains due to the selection only of the important principal components to be included in the model, further resulting to the deterioration of predictive ability of the model. We propose the principal components regression in a nonparametric framework to address the multicollinearity problem (and high dimensionality of predictors) while minimizing (or possibly eliminating) the specification bias that affect predictive ability of the model. The simulation study illustrated how the proposed nonparametric principal components regression address the multicollinearity problem and resolve the issue of high dimensionality while retaining higher predictive ability relative to parametric principal components regression model.

Keywords: Multicollinearity; Principal components regression; Nonparametric regression; High dimensional data

Biography: Erniel B. Barrios is a Professor of Statistics at the University of the Philippines Diliman. Research interests on computational statistics and nonparametric approaches in modeling and statistical inference. He is currently the editor of The Philippine Statistician, a professional journal published by the Philippine Statistical Association.