UC San Diego

Breakthroughs such as high-throughput sequencing are generating flourishing high-dimensional data that provoke challenges in both statistical analyses and interpretations. Since directly modeling such data often suffers from multiple testing and low power, an emerging alternative is to first reduce the dimension at the outset, by comparing two subjects’ genome sequences using dissimilarity metrics, yielding “between-subject attributes.” In the first half of this talk, I will extend the classical generalized linear models (GLM) to establish a new regression paradigm for between-subject attributes, using a class of semiparametric functional response models (FRM). Despite its growing applications, the efficiency of estimators for the FRM has not yet been carefully studied. This is of fundamental importance for semiparametric models due to the efficiency loss at the price of minimum model assumptions. For the next half of the talk, we leverage the Hilbert-Space-based semiparametric efficiency theory to show that estimators from a class of U-statistics-based generalized estimating equation (UGEE) achieve the semiparametric efficiency bound. Thus, like GEE for semiparametric GLM, UGEE estimators also harmonize efficiency and robustness, propelling growing applications in biomedical, psychosocial, and related research.