Before revision:  First, employing a carefully crafted coupling approach , we develop uniform distributional approximations for  t-statistic processes (indexed over the support of the conditioning variables).
After revision:  First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and develop feasible tuning parameter selection. Third, we develop pointwise inference methods based on undersmoothing and robust bias correction. Fourth, employing different coupling approaches , we develop uniform distributional approximations for t-statistic processes (indexed over the support of the conditioning variables).