Big Data Analysis Using Shrinkage Strategies

TL;DR

This paper introduces advanced shrinkage strategies for high-dimensional regression, significantly improving prediction accuracy in sparse models with more predictors than samples.

Contribution

It proposes a novel double shrinkage estimator that enhances prediction performance over existing methods like Lasso in high-dimensional settings.

Findings

Double shrunken estimators outperform traditional methods in simulations

Significant improvement in prediction accuracy on real datasets

Effective in models with many predictors and limited samples

Abstract

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse linear model some of the predictors have very weak influence on the response of interest. We propose to shrink estimators more than usual. Specifically, we use integrated estimation strategies in sub and full models and shrink the integrated estimators by incorporating a bounded measurable function of some weights. The exhibited double shrunken estimators improve the prediction performance of sub models significantly selected from existing Lasso-type variable selection methods. Monte Carlo simulation studies as well as real examples of eye data and Riboavin data confirm the superior performance of the estimators in the high-dimensional regression model.