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Fractional order statistic approximation for nonparametric conditional quantile inference

Matt Goldman, David M. Kaplan

arXiv 28 Sep 2016 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2016) · 11 citations (OpenAlex)

arXiv:1609.09035 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Fan, Y. and R. Liu (2016) A direct approach to inference in nonparametric and semiparametric quantile models0.95315687%
2Hutson, A. D (1999) Calculating nonparametric confidence intervals for quantiles using fractional order statistics0.909201075%
3Beran, R. and P. Hall (1993) Interpolated nonparametric prediction intervals and confidence intervals0.87452100%
4Kaplan, D. M (2015) Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion self0.84333100%
5Qu, Z. and J. Yoon (2015) Nonparametric estimation and inference on conditional quantile processes0.7373367%
6Goldman, M. and D. M. Kaplan (2016) Nonparametric inference on conditional quantile differences, linear combinations, and vectors, using $L$-statistics self0.73732100%
7Chaudhuri, P (1991) Nonparametric estimates of regression quantiles and their local Bahadur representation0.72116638%
8Bhattacharya, P. K. and A. K. Gangopadhyay (1990) Kernel and nearest-neighbor estimation of a conditional quantile0.6597329%
9Koenker, R (2012) quantreg: Quantile Regression0.6443267%
10Ho, Y. H. S. and S. M. S. Lee (2005) Calibrated interpolated confidence intervals for population quantiles0.64422100%

Showing the top 10 of 125 scored citations.