Before revision:  We propose a theoretical framework for analyzing small sample properties based on a novel approximation of the discontinuous sample moments with a H\"older continuous process . Using this approximation , we derive remainder bounds with nearly-optimal rates for the asymptotic linear expansions of exact and k-step estimators of IVQR models.
After revision:  First, we propose a higher-order analytical framework for comparing competing estimators in small samples and assessing the accuracy of common inference procedures. Our framework is based on a novel approximation of the discontinuous sample moments with a H\"older continuous process . Using this approximation , we derive remainder bounds with nearly-optimal rates for the asymptotic linear expansions of exact and k-step estimators of IVQR models.