inference-optimal band- width

Fractional order statistic approximation for nonparametric conditional quantile inference

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed confidence intervals for population quantiles using L-statistics as endpoints in Hutson (1999). We derive an analytic expression for the n−1 term, which may be used to calibrate the nominal coverage level to get O(n−3/2log(n)) coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles.

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