A Note on Estimation of a Distribution Function in a Nonparametric Set-up Using Stein’s Shrinkage Estimation Technique.

Based on Stein’s famous shrinkage estimation of a multivariate normal distribution, we propose a new type of estimators of the distribution function of a random variable in a nonparametric setup. The proposed estimators are then compared with the empirical distribution function, which is the best equivariant estimator under a well-known loss function. Our extensive simulation study shows that our proposed estimators can perform better for moderate to large sample sizes. [ABSTRACT FROM PUBLISHER]