A New Family of Distribution‐Free Geometric Shrinkage Variances Estimators With Applications

ABSTRACT In this paper, a family of geometric shrinkage variances estimators is derived under a new framework of Riemann manifold. Two approaches are proposed to estimate the optimal shrinkage parameter that minimizes a loss function defined as the square of a Riemann metric. Simulation studies show that the proposed estimators with the estimated optimal shrinkage parameter perform well under the percentage related improvement in average loss (PRIAL) criterion, which measures the degree of improvement over the naive sample variance estimators. Finally, the proposed estimators are applied to analyse a real data set of gene expression levels of cancer patients.