Yanglei Song (Queen's University)
Date
Thursday March 7, 20245:30 pm - 6:30 pm
Location
Jeffery Hall, Room 118Math Club
Thursday, March 7th, 2024
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: Yanglei Song (Queen's University)
Title: Stein's Paradox, Lemma, and Method
Abstract: Consider the estimation of three unrelated quantities, such as the speed of light, your daily coffee consumption, and Kingston's COVID activity level. The James–Stein estimator proposes to estimate them simultaneously and borrow information across them. For normally distributed data, it beats, in terms of the sum of quadratic losses, the most natural approach, which estimates each quantity individually. We prove this counter-intuitive result using Stein's lemma.
The reverse direction of Stein's lemma characterizes the standard normal distribution, It motivates a family of powerful techniques now called Stein's method for bounding distances between probability distributions. We discuss the basic idea behind the method.