Smooth quantile ratio estimation

Francesca Dominici, Leslie Cope, Daniel Q. Naiman, Scott L. Zeger

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 1.987 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.

Original languageEnglish (US)
Pages (from-to)543-557
Number of pages15
Issue number3
StatePublished - Sep 2005


  • Comparing means
  • Health expenditure
  • Log-normal
  • Order statistic
  • Q-Q plot
  • Regression spline
  • Smoking

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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