A1503
Title: Inference for projection parameters in linear regression: beyond $d = o(n^{1/2})$
Authors: Woonyoung Chang - Carnegi Mellon University (United States) [presenting]
Abstract: Inference for the projection parameters is studied in the random-design linear regression model with increasing dimensions and under minimal distributional assumptions. This problem has been studied under a variety of assumptions in the literature. When the dimension $d$ of the covariates is of smaller order than $n^{1/2}$, with $n$ denoting the sample size, it is known that the traditional Wald confidence intervals based on the asymptotic normality of the least squares estimator and the sandwich variance estimator are asymptotically valid. A bias correction is developed for the least squares estimator, and the asymptotic normality of the resulting debiased estimator is proved as long as $d = o(n^{2/3})$, with an explicit bound on the rate of convergence to normality. Recent methods of statistical inference that do not require an estimator of the variance to perform asymptotically valid statistical inference are leveraged. It is discussed how the techniques can be generalized to increase the allowable range of $d$ even further.
