A unified approach to likelihood inference on stochastic orderings in a nonparametric context

Journal of the American Statistical Association

Volumn 93, Issue 443, 1998, Pages 1112-1123

  Dardanoni, Valentino ^a   Forcina, Antonio ^b  

^a UNIVERSITY OF PALERMO   (Italy)

^b UNIVERSITY OF PERUGIA   (Italy)

Author keywords

Chi bar squared distribution; Likelihood inference; Likelihood ratio ordering; Order restricted inference; Stochastic ordering; Uniform ordering

Indexed keywords

EID: 0032342956     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10473772     Document Type: Article

References (39)

1. Agresti, A. (1984), Analysis of Ordinal Categorical Data, New York: Wiley.
2. Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972), Statistical Inference Under Order Restrictions, New York: Wiley.
3. Barlow, R. E., and Proschan, F. (1979), Statistical Theory of Reliability and Life Testing, New York: Holt, Rinehart and Winston.
4. Bartholomew, D. J. (1959), "A Test of Homogeneity for Ordered Alternatives," Biometrika, 46, 36-48.
5. Block, H. W., Sampson, A. R., and Savits, T. H. (1990), Topics in Statistical Dependence, IMS Lecture Notes-Monograph Series, Vol. 16, Hayward, CA: Institute for Mathematical Statistics.
6. Chemoff, H. (1954) "On the Distribution of the Likelihood Ratio," Annals of Mathematical Statistics, 25, 573-578.
7. Dobler, C. R (1994), "A Matrix Approach to Finding a Set of Generators and Finding the Polar (Dual) of a Class of Polyhedral Cones," SIAM Journal of Matrix Analysis and Applications, 15, 796-803.
8. Douglas, R., Fienberg, S. E., Lee, M. T., Sampson, A. R., and Whitaker, L. R. (1990), "Positive Dependence Concepts for Ordinal Contingency Tables," in Topics in Statistical Dependence, eds. H. W. Block, A. R. Sampson, and T. H. Savits. pp. 189-202 Hayward. CA: Institute for Mathematical Studies.
9. Dykstra, R. L. (1983), "An Algorithm for Restricted Least Squares," Journal of the American Statistical Association, 78, 837-842.
10. Dykstra, R. L. (1991), "Asymptotic Normality for Chi-Bar-Square Distributions," Canadian Journal of Statistics, 19, 297-306.
11. Dykstra, R. L., and Feltz, C. J. (1989). "Nonparametric Maximum Likelihood Estimation of Survival Functions With a General Stochastic Ordering and Its Dual," Biometrika, 76, 331-341.
12. Dykstra, R. L., Kochar, S., and Robertson, T. (1991), "Statistical Inference for Uniform Stochastic Ordering in Several Populations," The Annals of Statistics, 19, 870-888.
13. Dykstra, R. L., Kochar, S., and Robertson, T. (1995), "Inference for Likelihood Ratio Ordering in the TWo-Sample Problem," Journal of the American Statistical Association, 90, 1034-1040.
14. Fahrmeir, L., and J. Klinger (1994), "Estimating and Testing Generalized Linear Models Under Inequality Restrictions," mimeo.
15. Feltz, C. J., and Dykstra, R. L. (1985), "Maximum Likelihood Estimation of the Survival Function of N Stochastically Ordered Random Variables," Journal of the American Statistical Association, 80, 1012-1019.
16. Fienberg, S. E. (1980), The Analysis of Cross-Classsified Categorical Data, (2nd ed.), Cambridge, MA: MIT Press.
17. Goldman, S. M. and Ruud, P. A. (1993), "Nonparametric Multivariate Regression Subject to Constraint," mimeo.
18. Goodman, L. (1991), "Measures, Models and Graphical Displays in the Analysis of Cross-Classified Data," Journal of the American Statistical Association, 86, 1085-1111.
19. Gourieroux, C., Holly, A., and Monfort A. (1982), "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models With Inequality Constraints in the Regression Parameters." Econometrica, 50, 63-80.
20. Graybill, F. A. (1983), Matrices With Applications in Statistics, Belmont, CA: Wadsworth.
21. Grove, D. M. (1980). "A Test of Independence Against a Class of Ordered Alternatives in a 2 x C Contingency Table," Journal of the Americal Statistical Association, 75, 454-459.
22. logdeo, K. (1982), "Concepts of Dependence," in Encyclopedia of Statistical Sciences, eds. S. Kotz, and N. L. Johnson, New York: Wiley.
23. Lehmann, E. L. (1959), Testing Statistical Hypothesis, New York: Wiley.
24. Lehmann, E. L. (1966), "Some Concepts of Dependence," Annals of Mathematical Statistics, 37, 1137-1156.
25. Kodde, D. A., and Palm, F. C. (1986), "Wald Criteria for Jointly Testing Equality and Inequality Restrictions," Econometrica, 54, 1243-1248.
26. Kudo, A. (1963), "A Multivariate Analogue of the One-Sided Test," Biometrika, 50, 403-418.
27. McCullagh, P., and Nelder, J.A. (1989), Generalized Linear Models, New York: Chapman and Hall.
28. Perlman, M. D. (1969), "One-Sided Testing Problems in Multivariate Analysis," Annals of Mathematical Statistics, 40, 549-567.
29. Raubertas, R. F., Nordheim, E. V., and Lee, C. C. (1986), "Hypothesis Test for Normal Means Constrained by Linear Inequalities," Communications in Statistics; Part A-Theory and Methods, 15, 2809-2833.
30. Robertson, T. and Wright, F. T. (1981), "Likelihood Ratio Tests for and Against Stochastic Ordering Between Multinomial Populations," The Annals of Statistics, 9, 1248-1257.
31. Robertson, T. and Wright, F. T (1982), "Bounds on Mixtures of Distributions Arising in Order Restricted Inference," The Annals of Statistics, 10, 302-306.
32. Robertson, T., Wright, F. T., and Dykstra, R. (1988), Order Restricted Statistical Inference, New York: Wiley.
33. Sasabuchi, S. (1980), "A Test of a Multivariate Normal Mean With Composite Hypotheses Determined by Linear Inequalities," Biometrika, 67, 429-439.
34. Shaked, M. (1977), "A Family of Concepts of Dependence for Bivariate Distributions," Journal of the Americal Statistical Association, 72, 642-650.
35. Shaked, M., and Shanthikumar, J.G. (1994), Stochastic Orders and Their Applications, San Diego: Academic Press.
36. Shapiro, A. (1985), "Asymptotic Distribution of Test Statistics in the Analysis of Moment Structures Under Inequality Constraints," Biometrika, 72, 133-144.
37. Shapiro, A. (1988), 'Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis," International Statistical Review, 56, 49-62.
38. Wang, Y. (1996), "A Likelihood Ratio Test Against Stochastic Ordering in Several Populations," Journal of the Americal Statistical Association, 91, 1676-1683.
39. Wolak, F. A. (1991), 'The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, 59, 981-995.