Inference for Median and a Generalization of HulC
arxiv(2024)
摘要
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. Our study breaks new ground by investigating the width of these
intervals under non-standard assumptions. Surprisingly, we find that properly
scaled, the interval width converges to a non-degenerate random variable,
unlike traditional intervals. We also adapt our findings for constructing
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.
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