On Semiparametric Efficiency of an Emerging Class of Regression Models for Between-subject Attributes

Music City Center 

Semiparametric functional response models for between-subject, or pairwise, at- tributes are attracting attention owing to their robustness in inference, feasibility in computation, and versatility in interpreting rank-based and high-dimensional variables. This paper develops the semiparametric efficiency bound for this emerging class of regressions whose modeling units are pairwise observations violating independence. To handle their correlations in making inferences, the U-statistics-based generalized estimating equations (UGEE) have been previously established to pro- vide consistent and asymptotically normal estimators. They demonstrated promising performances in simulations and various applications, including microbiome and neuroimaging studies. However, a vital gap is their understudied asymptotic efficiency, which is the key to ensuring optimality and sensitivity in signal detection. Albeit the thoroughly studied semiparametric efficiency in the traditional setting for i.i.d. observations, the efficiency bound for pairwise attributes remains open. By enriching the theory built upon Hilbert spaces, we showed that UGEE estimators are asymptotically efficient. Essentially, our developed theory will not only fill the critical gap in efficiency for this emerging model class but propel applications availing this optimal inference technique. More importantly, this work will serve as a building block for future efficiency development in more complex settings such as missing data in longitudinal studies.