Events
DMS Statistics and Data Science Seminar 
Time: Oct 25, 2023 (02:00 PM) 
Location: 354 Parker Hall / ZOOM 
Details: Speaker: Dr. Yanyuan Ma (Penn State University)
Title: Doubly Flexible Estimation under Label Shift
Abstract: In studies ranging from clinical medicine to policy research, complete data are usually available from a population P, but the quantity of interest is often sought for a related but different population Q which only has partial data. In this paper, we consider the setting that both outcome Y and covariate X are available from P whereas only X is available from Q, under the socalled label shift assumption, i.e., the conditional distribution of X given Y remains the same across the two populations. To estimate the parameter of interest in population Q via leveraging the information from population P, the following three ingredients are essential: (a) the common conditional distribution of X given Y, (b) the regression model of Y given X in population P, and (c) the density ratio of the outcome Y between the two populations. We propose an estimation procedure that only needs some standard nonparametric regression technique to approximate the conditional expectations with respect to (a), while by no means needs an estimate or model for (b) or (c); i.e., doubly flexible to the possible model misspecifications of both (b) and (c). This is conceptually different from the wellknown doubly robust estimation in that, double robustness allows at most one model to be misspecified whereas our proposal here can allow both (b) and (c) to be misspecified. This is of particular interest in our setting because estimating (c) is difficult, if not impossible, by virtue of the absence of the Ydata in population Q. Furthermore, even though the estimation of (b) is sometimes offtheshelf, it can face the curse of dimensionality or computational challenges. We develop the large sample theory for the proposed estimator and examine its finitesample performance through simulation studies as well as an application to the MIMICIII database.
