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Fractional order statistic approximation for nonparametric conditional quantile inference

Listed author(s):
  • Goldman, Matt
  • Kaplan, David M.

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed (Hutson, 1999) 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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304407616301944
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 196 (2017)
Issue (Month): 2 ()
Pages: 331-346

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Handle: RePEc:eee:econom:v:196:y:2017:i:2:p:331-346
DOI: 10.1016/j.jeconom.2016.09.015
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. David M. Kaplan & Matt Goldman, 2011. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1620, Department of Economics, University of Missouri, revised 21 Nov 2016.
  2. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
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  5. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles," Working Papers 13-19, Department of Economics, University of Missouri, revised Nov 2016.
  6. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
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  8. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
  9. Yao, Qiwei & Polonik, Wolfgang, 2002. "Set-indexed conditional empirical and quantile processes based on dependent data," LSE Research Online Documents on Economics 5878, London School of Economics and Political Science, LSE Library.
  10. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.
  11. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
  12. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
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  16. Sule Alan & Thomas Crossley & Paul Grootendorst & Michael Veall, 2005. "Distributional effects of `general population' prescription drug programs in Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 38(1), pages 128-148, February.
  17. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.
  18. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
  19. Manning, Willard G. & Blumberg, Linda & Moulton, Lawrence H., 1995. "The demand for alcohol: The differential response to price," Journal of Health Economics, Elsevier, vol. 14(2), pages 123-148, June.
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  21. Jason Abrevaya, 2001. "The effects of demographics and maternal behavior on the distribution of birth outcomes," Empirical Economics, Springer, vol. 26(1), pages 247-257.
  22. Jones, M. C., 2002. "On fractional uniform order statistics," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 93-96, May.
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