The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that sample mean, classically regarded as “usual estimator”, may be suboptimal dimensions. development James-Stein estimator, addresses this paradox, by now inspired a large literature on theme “shrinkage” In direction, we develop type estimator for first principal component dimension...

Entropy is a fundamental quantity in statistics and machine learning. In this note, we present a novel procedure for statistical learning of entropy from high-dimensional small-sample data. Specifically, we introduce a a simple yet very powerful small-sample estimator of the Shannon entropy based on James-Stein-type shrinkage. This results in an estimator that is highly efficient statistically ...

In a two-stage linear regression model with Normal noise, I consider James–Stein type shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I show that the standard two-stage least-squares estimator is dominated with respect to bias. I construct the dominating estimator by a variant of James...

The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that sample mean, classically regarded as usual estimator, may be suboptimal dimensions. development James-Stein addresses this paradox, by now inspired a large literature on theme shrinkage In direction, we develop type estimator for first principal component dimension and low size d...

The authors consider the problem of estimating, under quadratic loss, the mean of a spherically symmetric distribution when its norm is supposed to be known and when a residual vector is available. They give a necessary and sufficient condition for the optimal James-Stein estimator to dominate the usual estimator. Various examples are given that are not necessarily variance mixtures of normal d...

The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I...