Development of Shrinkage Methods in Estimation—High Dimensional Analysis and Small Area Estimation—

Abstract

In the high-dimensional analysis, usual estimation procedures yield large estimation errors because sample sizes are small as compared with the number of unknown parameters. Also in the small-area estimation, the sample means of small-areas have large estimation errors since the sample sizes from individual areas are small. In this case, shrinkage estimators are known as stable procedures with higher precision, because the shrinkage estimators can be obtained by shrinking the usual estimators toward stable estimators which are derived under some reasonable assumptions. In this paper, usefulness of shrinkage procedures is explained from applied aspects in high-dimensional analysis and small area estimation.