• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.151-156
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• 2003

Variable selection algorithm for principal component analysis using penalized likelihood method is proposed. We will adopt a probabilistic principal component idea to utilize likelihood function for the problem and use HARD penalty function to force coefficients of any irrelevant variables for each component to zero. Consistency and sparsity of coefficient estimates will be provided with results of small simulated and illustrative real examples.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.41-54
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• 2015

In this article, we propose nonconcave penalties on a reduced-rank regression model to select variables and estimate coefficients simultaneously. We apply HARD (hard thresholding) and SCAD (smoothly clipped absolute deviation) symmetric penalty functions with singularities at the origin, and bounded by a constant to reduce bias. In our simulation study and real data analysis, the new method is compared with an existing variable selection method using $L_1$ penalty that exhibits competitive performance in prediction and variable selection. Instead of using only one type of penalty function, we use two or three penalty functions simultaneously and take advantages of various types of penalty functions together to select relevant predictors and estimation to improve the overall performance of model fitting.