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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. Roger Newson, 2007. "Robust confidence intervals for Hodges–Lehmann median difference," United Kingdom Stata Users' Group Meetings 2007 01, Stata Users Group.
    4. 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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    8. Roger Newson, 2016. "The role of Somers's D in propensity modeling," United Kingdom Stata Users' Group Meetings 2016 01, Stata Users Group.
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    18. Yongzheng Wang & Xinchen Gu & Haoran Yu, 2023. "Spatiotemporal Variation in the Yangtze River Delta Urban Agglomeration from 1980 to 2020 and Future Trends in Ecosystem Services," Land, MDPI, vol. 12(4), pages 1-20, April.
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    21. Roger Newson, 2019. "Bland–Altman plots, rank parameters, and calibration ridit splines," London Stata Conference 2019 01, Stata Users Group.
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    23. Roger Newson, 2015. "Somers' D: A common currency for associations," United Kingdom Stata Users' Group Meetings 2015 01, Stata Users Group.

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