##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Larry Goldstein

#### University of Southern California

## Zero bias enhanced Stein couplings for normal approximation

##### Abstract:

Stein's method for distributional approximation has become a valuable tool in probability and statistics by providing finite sample distributional bounds for a wide class of target distributions in a number of metrics. A key step in popular versions of the method involves making couplings constructions, and a family of couplings of Chen and Roellin vastly expanded the range of applications for which Stein's method for normal approximation could be applied. This family subsumes both Stein's classical exchangeable pair, and the size bias coupling. A further simple generalization includes zero bias couplings, and also allows for situations where the coupling is not exact. The zero bias versions result in bounds for which often tedious computations of a variance of a conditional expectation is not required. An example to the Lightbulb process shows that even though the method may be simple to apply, it may yield improvements over previous results that had achieved bounds with optimal rates and small, explicit constants.

Host: Todd Kemp

### October 13, 2022

### 11:00 AM

APM 6402 with live streaming via Zoom

Zoom ID: 947 1948 3503

Email poagarwal@ucsd.edu for password

Research Areas

Probability Theory****************************