| This dissertation concerns methods for inference on quantiles in various models. Methods that are asymptotically justified may still be quite inaccurate in finite samples. To improve the state of the art, I explore different theoretical approaches for achieving higher-order accuracy: fractional order statistic theory based on exact finite-sample distributions in Chapters 1 and 2, and Edgeworth expansions and fixed-smoothing asymptotics in Chapter 3. For each of the different practical methods proposed, I examine accuracy via precise theoretical results as well as simulations. The family of methods using interpolated duals of exact-analytic L-statistics (IDEAL) covers unconditional (one-sample and two-sample treatment/control, Ch. 1) and nonparametric conditional (Ch. 2) models, and it offers improvements over the existing literature in terms of accuracy, robustness, and/or computation time. The Edgeworth-based method improves upon related prior methods and is a good alternative for quantiles too far into the tails for IDEAL to handle. |
