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Smooth quantile ratio estimation

Author

Listed:
  • Francesca Dominici
  • Leslie Cope
  • Daniel Q. Naiman
  • Scott L. Zeger

Abstract

We propose a novel approach to estimating the mean difference between two highly skewed distributions. The method, which we call smooth quantile ratio estimation, smooths, over percentiles, the ratio of the quantiles of the two distributions. The method defines a large class of estimators, including the sample mean difference, the maximum likelihood estimator under log-normal samples and the L-estimator. We derive asymptotic properties such as consistency and asymptotic normality, and also provide a closed-form expression for the asymptotic variance. In a simulation study, we show that smooth quantile ratio estimation has lower mean squared error than several competitors, including the sample mean difference and the log-normal parametric estimator in several realistic situations. We apply the method to the 1987 National Medicare Expenditure Survey to estimate the difference in medical expenditures between persons suffering from the smoking attributable diseases, lung cancer and chronic obstructive pulmonary disease, and persons without these diseases. Copyright 2005, Oxford University Press.

Suggested Citation

  • Francesca Dominici & Leslie Cope & Daniel Q. Naiman & Scott L. Zeger, 2005. "Smooth quantile ratio estimation," Biometrika, Biometrika Trust, vol. 92(3), pages 543-557, September.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:543-557
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    File URL: http://hdl.handle.net/10.1093/biomet/92.3.543
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    Cited by:

    1. Fabian Dunker & Stephan Klasen & Tatyana Krivobokova, 2017. "Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions," Papers 1710.09009, arXiv.org.
    2. P. B. Kenfac Dongmezo & P. N. Mwita & I. R. Kamga Tchwaket, 2017. "Imputation Based Treatment Effect Estimators," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(3), pages 1-2.
    3. Dandan Xu & Michael J. Daniels & Almut G. Winterstein, 2018. "A Bayesian nonparametric approach to causal inference on quantiles," Biometrics, The International Biometric Society, vol. 74(3), pages 986-996, September.
    4. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.

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