Big Data Analysis Using Shrinkage Strategies

2017/04/17 by Yuzbasi, B., ‎M‎ohammad Arashi, Arashi, M. +2
Environmental Science · Mathematics · #FOS: Computer and information sciences #Hydrology and Watershed Management Studies #Methodology (stat.ME) #Soil Geostatistics and Mapping #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1704.05074

openalex publication_date 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• Least angle regression
• The horseshoe estimator for sparse signals
• Double shrunken selection operator

Related

• Linear shrinkage for predicting responses in large-scale multivariate linear regression
• Nearly optimal Bayesian Shrinkage for High Dimensional Regression
• Multi-Target Shrinkage
• Bayesian Approaches to Shrinkage and Sparse Estimation
• Bayesian sparse multiple regression for simultaneous rank reduction and variable selection