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Fractional order statistic approximation for nonparametric conditional quantile inference

Matt Goldman and David Kaplan ()

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Abstract: 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 $O\bigl(n^{-3/2}[\log(n)]^3\bigr)$ coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations. Code is available from the second author's website for both unconditional and conditional methods, simulations, and empirical examples.

Date: 2016-09
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Published in Journal of Econometrics 196 (2017) 331-346

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http://arxiv.org/pdf/1609.09035 Latest version (application/pdf)

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Journal Article: Fractional order statistic approximation for nonparametric conditional quantile inference (2017) Downloads
Working Paper: Fractional order statistic approximation for nonparametric conditional quantile inference (2016) Downloads
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