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Fractional order statistic approximation for nonparametric conditional quantile inference. (English) Zbl 1403.62045

Summary: Using and extending fractional order statistic theory, we characterize the \(O(n^{-1})\) coverage probability error of the previously proposed [A. D. Hutson, J. Appl. Stat. 26, No. 3, 343–353 (1999; Zbl 1072.62577)] confidence intervals for population quantiles using \(L\)-statistics as endpoints. We derive an analytic expression for the \(n^{-1}\) term, which may be used to calibrate the nominal coverage level to get \(O(n^{-3/2}[\log(n)]^3)\) 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 provided for both unconditional and conditional inference.

MSC:

62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions

Citations:

Zbl 1072.62577

Software:

SemiPar; quantreg
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Full Text: DOI arXiv

References:

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