. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We establish existence of Stein kernels for probability measures on R satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W2 with optimal rate and dependence on the dimension. As a byproduct, we obtain a stable version of an estimate of the Po...

Charles Stein [10] discovered that, under quadratic loss, the usual unbiased estimator for the mean vector of a multivariate normal distribution is inadmissible if the dimension n of the mean vector exceeds two. On the way, he constructed shrinkage estimators that dominate the usual estimator asymptotically in n. It has since been claimed that Stein’s results and the subsequent James–Stein esti...

We construct infinitely many distinct simply connected Stein fillings of a certain infinite family of contact 3-manifolds. Math. Res. Lett. 15 (2008), no. 6, 1127–1132 c © International Press 2008 A NOTE ON STEIN FILLINGS OF CONTACT MANIFOLDS Anar Akhmedov, John B. Etnyre, Thomas E. Mark, and Ivan Smith Abstract. In this note we construct infinitely many distinct simply connected Stein fillings...