Least square and Empirical Bayes Approaches for Estimating Random Change Points

Abstract

Here we develop methods for applications where random change points are known to be present a priori and the interest lies in their estimation and investigating risk factors that influence them. A simple least square method estimating each individual’s change point based on one’s own observations is first proposed. An easy-to-compute empirical Bayes type shrinkage is then proposed to pool information from separately estimated change points. A method to improve the empirical Bayes estimates is developed. Simulations are conducted to compare least-square estimates and Bayes shrinkage estimates. The proposed methods are applied to the Berkeley Growth Study data to estimate the transition age of the puberty height growth.