A1502
Title: Inference for median and a generalization of HulC
Authors: Manit Paul - Wharton School, University of Pennsylvania (United States) [presenting]
Arun Kuchibhotla - Carnegie Mellon University (United States)
Abstract: Constructing distribution-free confidence intervals for the median, a classic problem in statistics has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval width. New ground is broken by investigating the width of these intervals under non-standard assumptions. Surprisingly, it is found that when properly scaled, the interval width converges to a non-degenerate random variable, unlike traditional intervals. The findings are also adapted to construct improved confidence intervals for general parameters, enhancing the existing HulC procedure. These advances provide practitioners with more robust tools for data analysis, reducing the need for strict distributional assumptions.
