Tests For and Against a Positive Dependence Restriction in Two-Way Ordered Contingency Tables

  • Oh, Myongsik (Department of Statistics, Pusan University of Foreign Studies)
  • Published : 1998.06.01

Abstract

Dependence concepts for ordered two-way contingency tables have been of considerable interest. We consider a dependence concept which is less restrictive than likelihood ratio dependence and more restrictive than regression dependence. Maximum likelihood estimation of cell probability under this dependence restriction is studied. The likelihood ratio statistics for and against this dependence are proposed and their large sample distributions are derived. A real data is analyzed to illustrate the estimation and testing procedures.

Keywords

References

  1. Journal of Multivariate Analysis v.36 Tests for independence in contingency tables with ordered categoties Cohen, A.;H.B.Sachrowitz
  2. Topics in Statistical Dependence Positive dependence concepts for ordinal contingency tables Douglas, R.;S. E. Fienberg;M. T. Lee;A. R. Sampson;L. R. Whitaker
  3. Journal of the American Statistical Association v.83 Duality of I projections and Maximum likelihood estimation for log-linear models under cone constraints Dykstra, R. L.;J.H. Lemke
  4. The Annals of Sraristics v.19 Statistical ingerence for uniform stochastic ordering in several populations Dykstra, R. L.;S. C. Kochar;T. Robertson
  5. Journal of the American Statistical Association v.80 Maximum likelihood estimation of the survial functions of N stochastically ordered rendom variables Feltz, P.D.;R.L.Dykstra
  6. Biometrika v.69 Use of cumulative efficient scores for testing ordered alternatives in discrete models Hirotsu, C.
  7. Topics in Statistical Dependence Tests of independence against likelihood ratio dependence in ordered contingency tables Lee, M. -L. T.;H. W. Block(ed.);A. R. Sampson(ed.);T. H. Savit(ed.)
  8. Annals of Mathematical Satistics v.37 Some concepts of dependence Lehmann, E. L.
  9. Naval Research Logistics Quarterly v.34 Testing for positive quadrant dependence in ordinal contingency table Nguyen, T.;A. R. Sampson
  10. Ph. D. Thesis, The University of Iowa Statistical tests concerning a set of multinomial parameters under order restrictions: Approximations to mull hypotheses distributions Oh, M.
  11. Communicatiosn in Statistics-Theory and Methods v.24 no.8 On maximum likelihood estimation of cell probabilities in $2{\times}k $ contingency tables under negative dependence restrictions with vatious sampling scheme Oh, M.
  12. Approximate tests for uniform stochastic ordering in several multinomial populations Oh, M.
  13. The Canadian Journal of Statistics v.26 Goodness-of-fit test for uniform stoxhastic ordering among several distributions Park, C.G.;C. I. C. Lee;T. Robertson
  14. Applied Statistics v.31 Exact tests for trends in ordered contingency tables Patefedld, W. M.
  15. The Annals of Statistics v.10 Bounds on mixtures of distribution arising in order restricted inference Robertson, T.;F. T. Wright
  16. Biometrika v.70 On approximation of the level probabilities and associated distributions in order restricted inference Robertson, T.;F. T. Wright
  17. Order Restricted Statistical Inference Robertson, T.;F. T. Wright;R. L. Dykstra
  18. Journal of the American Stratistical Association v.72 A family of concepts of dependence for bivariate distributions Shaked, M.
  19. The Midtown Manhattan Study rev. ed. Mental Health in the Metropolis Srole, L.;T. S. Langner;S. T. Michael;P. Kirkpatrick;M. K. Opler;T. A. C. Rennie