A1855
Title: Hypothesis testing for penalized estimating equations with cross-fitted covariance calibration
Authors: Jing Zhou - University of Manchester (United Kingdom) [presenting]
Zhe Zhang - University of Pennsylvania (United States)
Abstract: Hypothesis testing for penalized estimators is studied in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional heteroscedastic regression. Assuming that the conditional mean model is correctly specified, it is established that the penalized estimating equations admit a $\sqrt{n}$-consistent solution, even when the working covariance structure is misspecified. The inferential target is a low-dimensional subvector of parameters associated with the mean model. The resulting test statistic is shown to converge to a $\chi^2$ distribution, and its asymptotic power depends on the nuisance covariance function. To mitigate this dependence, a procedure for estimating the covariance function via cross-fitting is proposed, which provides a calibrated and robust approach for inference.
