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Weighted U-statistics for likelihood-ratio ordering of bivariate data

Author

Listed:
  • Sangita Kulathinal

    (University of Helsinki)

  • Isha Dewan

    (Indian Statistical Institute)

Abstract

Characterisation of marginal distribution and density functions is of interest where data on a pair of random variables (X, Y) are observed. Stochastic orderings between (X, Y) have been studied in statistics and economics. Likelihood-ratio ordering is useful in understanding the behaviour of the random variables. In this article, tests based on U-statistics are proposed to test for equality of marginal density functions against the alternative of likelihood-ratio ordered when (X, Y) are dependent. The tests can be used when the data are either completely observed or subjected to independent univariate right censoring. The asymptotic variances of these tests are complicated and hence, are estimated using jackknife variance estimators. Validity of the jackknife variance estimators in statistical inference based on the proposed tests is demonstrated using simulation studies. The test for uncensored setting has desired size and good power for small sample. The performance of the tests for censored case depends on the sample size, proportion of censoring and the measure of dependence between X and Y. The tests are illustrated on three real data sets chosen in order to bring out various aspects of the tests.

Suggested Citation

  • Sangita Kulathinal & Isha Dewan, 2023. "Weighted U-statistics for likelihood-ratio ordering of bivariate data," Statistical Papers, Springer, vol. 64(2), pages 705-735, April.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01332-w
    DOI: 10.1007/s00362-022-01332-w
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    References listed on IDEAS

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    1. Roosen J. & Hennessy D.A., 2004. "Testing for the Monotone Likelihood Ratio Assumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 358-366, July.
    2. Alan D. Hutson, 2016. "Nonparametric rank based estimation of bivariate densities given censored data conditional on marginal probabilities," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-14, December.
    3. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    4. N. Unnikrishnan Nair & P. G. Sankaran & Preethi John, 2018. "Modelling bivariate lifetime data using copula," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 133-153, August.
    5. Tao Yu & Pengfei Li & Jing Qin, 2017. "Density estimation in the two-sample problem with likelihood ratio ordering," Biometrika, Biometrika Trust, vol. 104(1), pages 141-152.
    6. Christopher A. Carolan & Joshua M. Tebbs, 2005. "Nonparametric tests for and against likelihood ratio ordering in the two-sample problem," Biometrika, Biometrika Trust, vol. 92(1), pages 159-171, March.
    7. Beare, Brendan K. & Moon, Jong-Myun, 2015. "Nonparametric Tests Of Density Ratio Ordering," Econometric Theory, Cambridge University Press, vol. 31(3), pages 471-492, June.
    8. Rondeau, Virginie & Marzroui, Yassin & Gonzalez, Juan R., 2012. "frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i04).
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