An Adaptive Test for Ordered Interqartile Ranges among Several Distributions

  • Park, Chul-Gyu (Department of Applied Statistics, University of Suwon)
  • Published : 2001.03.01

Abstract

An adaptive estimation and testing method is proposed for comparing dispersions among several ordered groups. Based upon the large sampling theory for nonparametric quartile estimators, we derive the order restricted estimators and construct a simple test statistic. This test statistic has a mixture of several chi-square distributions as its asymptotic null distribution. The proposed test is illustratively applied to survival time data for the patients with carcinoma of the oropharynx.

Keywords

References

  1. Annals of Mathematical Statistics v.34 Efficient utilization of non-numerical information in quantitative analysis;general theory and the case of the simple order Abelson, R. P.;Tukey, J. W.
  2. Statistics and Probability Letters v.7 Testing for dispersive ordering Ahmad, I. A.;Kochar, S. C.
  3. Biometrika v.46 A test of homogeneity for ordered alternatives Bartholomew, D. J.
  4. Biometrika v.61 On testing for ordered alternative with increased sample sizes for a control Chase, G. R.
  5. Annals of Statistics v.19 Statistical inference for uniform stochastic ordering in several populations Dykstra, R. L.;Kochar, S.;Robertson, T.
  6. Communications in Statistics - Theory and Methods v.16 A two sample ordered alternative test for means and variances Halperin, M.;Gordon, K. K.
  7. Advances in Order Restricted Statistical Infernce (ed.) A class of distribution-free tests for testing homogeneity of variances against ordered alternativea Kochar, S. C.;Gupta, R. P.;Dykstra, R. L.;Robertson, T.;Wright, F. T.
  8. Linear and Nonlinear Programming Luenberger, D. G.
  9. Journal of the American Statistical Association v.82 Comparison of several treatments with a control using multiple contrasts Mukerjee, H.;Robertson, T.;Wright, F. T.
  10. The Canadian Journal of Statistics v.26 Goodness-of-fit test for uniform stochastic ordering among several distributions Park, C. C.;Lee, C. I. C.;Robertson, T.
  11. Annals of Statistics v.9 Likelihood ratio tests for and against stochastic ordering between multinomial populations Robertson, T.;Wright, F. T.
  12. Order Restricted Statistical Inference Robertson, T.;Wright, F. T.;Dykstra, R. L.
  13. Annals of Mathematical Statistics v.37 Most stringent somewhere most powerful test against alternatives restricted by a number of linear inequalities Schaafsma, W.;Smid, L. J.
  14. Approximation Theorems of Mathematical Statistics Serfling, R. J.
  15. Biometrika v.83 Testing for ordered group effects with repeated measurements Shin, D. W.;Park, C. G.;Park, T.
  16. Density Estimation for Statistics and Data Analysis Silverman, B. W.
  17. Kernel Smoothing Wand, M. O.;Jones, M. C.
  18. Journal of American Statistical Association v.91 A likelihood ratio test against stochastic ordering in several populations Wang, Y.