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Confidence intervals for rank statistics: Percentile slopes, differences, and ratios

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  • Roger Newson

    (Imperial College London)

Abstract

I present a program, censlope, for calculating confidence intervals for generalized Theil–Sen median (and other percentile) slopes (and per-unit ratios) of Y with respect to X. The confidence intervals are robust to the possibility that the conditional population distributions of Y, given different values of X, differ in ways other than location, such as having unequal variances. censlope uses the program somersd and is part of the somersd package. censlope can therefore estimate confounder-adjusted percentile slopes, limited to comparisons within strata defined by values of confounders, or by values of a propensity score representing multiple confounders. Iterative numerical methods have been implemented in the Mata language, enabling efficient calculation of percentile slopes and their confidence limits in large samples. I give example analyses from the auto dataset and from the Avon Longitudinal Study of Pregnancy and Childhood (ALSPAC). Copyright 2006 by StataCorp LP.

Suggested Citation

  • Roger Newson, 2006. "Confidence intervals for rank statistics: Percentile slopes, differences, and ratios," Stata Journal, StataCorp LP, vol. 6(4), pages 497-520, December.
    • Handle: RePEc:tsj:stataj:v:6:y:2006:i:4:p:497-520
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    1. Roger Newson, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 309-334, September.
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    Cited by:

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    2. Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928, arXiv.org, revised Mar 2010.
    3. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.
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    5. Roger Newson, 2016. "The role of Somers's D in propensity modeling," United Kingdom Stata Users' Group Meetings 2016 01, Stata Users Group.
    6. Jeannette Brosig‐Koch & Heike Hennig‐Schmidt & Nadja Kairies‐Schwarz & Daniel Wiesen, 2017. "The Effects of Introducing Mixed Payment Systems for Physicians: Experimental Evidence," Health Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 243-262, February.
    7. Ahdesmäki Miika & Lancashire Lee & Proutski Vitali & Wilson Claire & Davison Timothy S. & Harkin D. Paul & Kennedy Richard D., 2013. "Model selection for prognostic time-to-event gene signature discovery with applications in early breast cancer data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 619-635, October.
    8. Ichiro Kunitsugu & Masayuki Okuda & Shinichi Sugiyama & Norikazu Yoshitake & Yukio Tanizawa & Satoshi Sasaki & Tatsuya Hobara, 2012. "Meat intake frequency and anemia in Japanese children and adolescents," Nursing & Health Sciences, John Wiley & Sons, vol. 14(2), pages 197-203, June.
    9. Alena MINÃ ROVÃ, 2012. "Evaluation Of Dependence Of Occurrence Of Risk Events In Logistics On Risk Factors By Means Of Somers' D Coefficient," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 7(1(19)/ Sp), pages 73-86.
    10. Orth, Walter, 2012. "The predictive accuracy of credit ratings: Measurement and statistical inference," International Journal of Forecasting, Elsevier, vol. 28(1), pages 288-296.
    11. Roger Newson, 2019. "Bland–Altman plots, rank parameters, and calibration ridit splines," London Stata Conference 2019 01, Stata Users Group.
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    18. Hanna Karolina Szymborska, 2018. "Household wealth structures and position in the income distribution – econometric analysis for the USA, 1989-2013," Working Papers PKWP1806, Post Keynesian Economics Society (PKES).
    19. Marszalec, Daniel, 2018. "Fear not the simplicity - An experimental analysis of auctions for complements," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 81-97.
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