A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context

References

• Agresti , A. 1984 . Analysis of Ordinal Categorical Data , New York : Wiley .
   Google Scholar
• Barlow , R. E. , Bartholomew , D. J. , Bremner , J. M. and Brunk , H. D. 1972 . Statistical Inference Under Order Restrictions , New York : Wiley .
   Google Scholar
• Barlow , R. E. and Proschan , F. 1979 . Statistical Theory of Reliability and Life Testing , New York : Holt, Rinehart and Winston .
   Google Scholar
• Bartholomew , D. J. 1959 . “A Test of Homogeneity for Ordered Alternatives,” . Biometrika , 46 : 36 – 48 .
   Web of Science ®Google Scholar
• Block , H. W. , Sampson , A. R. and Savits , T. H. 1990 . Topics in Statistical Dependence , Vol. 16 , Hayward , CA : Institute for Mathematical Statistics . IMS Lecture Notes-Monograph Series
   Google Scholar
• Chernoff , H. 1954 . “On the Distribution of the Likelihood Ratio,” . Annals of Mathematical Statistics , 25 : 573 – 578 .
   Google Scholar
• Dobler , C. P. 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 .
   Web of Science ®Google Scholar
• 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 , Edited by: Block , H. W. , Sampson , A. R. and Savits , T. H. 189 – 202 . Hayward , CA : Institute for Mathematical Studies .
   Google Scholar
• Dykstra , R. L. 1983 . “An Algorithm for Restricted Least Squares,” . Journal of the American Statistical Association , 78 : 837 – 842 .
   Web of Science ®Google Scholar
• Dykstra , R. L. 1991 . “Asymptotic Normality for Chi-Bar-Square Distributions,” . Canadian Journal of Statistics , 19 : 297 – 306 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Fahrmeir , L. and Klinger , J. 1994 . “Estimating and Testing Generalized Linear Models Under Inequality Restrictions,” mimeo
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Fienberg , S. E. 1980 . The Analysis of Cross-Classsified Categorical Data, , 2nd ed. , Cambridge , MA : MIT Press .
   Google Scholar
• Goldman , S. M. and Ruud , P. A. 1993 . “Nonparametric Multivariate Regression Subject to Constraint,” mimeo
   Google Scholar
• Goodman , L. 1991 . “Measures, Models and Graphical Displays in the Analysis of Cross-Classified Data,” . Journal of the American Statistical Association , 86 : 1085 – 1111 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Graybill , F. A. 1983 . Matrices With Applications in Statistics , Belmont , CA : Wadsworth .
   Google Scholar
• Grove , D. M. 1980 . “A Test of Independence Against a Class of Ordered Alternatives in a 2 × C Contingency Table,” . Journal of the Americal Statistical Association , 75 : 454 – 459 .
   Web of Science ®Google Scholar
• Jogdeo , K. 1982 . “Concepts of Dependence,” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. New York : Wiley .
   Google Scholar
• Lehmann , E. L. 1959 . Testing Statistical Hypothesis , New York : Wiley .
   Google Scholar
• Lehmann , E. L. 1966 . “Some Concepts of Dependence,” . Annals of Mathematical Statistics , 37 : 1137 – 1156 .
   Google Scholar
• Kodde , D. A. and Palm , F. C. 1986 . “Wald Criteria for Jointly Testing Equality and Inequality Restrictions,” . Econometrica , 54 : 1243 – 1248 .
   Web of Science ®Google Scholar
• Kudo , A. 1963 . “A Multivariate Analogue of the One-Sided Test,” . Biometrika , 50 : 403 – 418 .
   Web of Science ®Google Scholar
• McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models , New York : Chapman and Hall .
   Google Scholar
• Perlman , M. D. 1969 . “One-Sided Testing Problems in Multivariate Analysis,” . Annals of Mathematical Statistics , 40 : 549 – 567 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Robertson , T. and Wright , F. T. 1982 . “Bounds on Mixtures of Distributions Arising in Order Restricted Inference,” . The Annals of Statistics , 10 : 302 – 306 .
   Web of Science ®Google Scholar
• Robertson , T. , Wright , F. T. and Dykstra , R. 1988 . Order Restricted Statistical Inference , New York : Wiley .
   Google Scholar
• Sasabuchi , S. 1980 . “A Test of a Multivariate Normal Mean With Composite Hypotheses Determined by Linear Inequalities,” . Biometrika , 67 : 429 – 439 .
   Web of Science ®Google Scholar
• Shaked , M. 1977 . “A Family of Concepts of Dependence for Bivariate Distributions,” . Journal of the Americal Statistical Association , 72 : 642 – 650 .
   Web of Science ®Google Scholar
• Shaked , M. and Shanthikumar , J. G. 1994 . Stochastic Orders and Their Applications , San Diego : Academic Press .
   Google Scholar
• Shapiro , A. 1985 . “Asymptotic Distribution of Test Statistics in the Analysis of Moment Structures Under Inequality Constraints,” . Biometrika , 72 : 133 – 144 .
   Web of Science ®Google Scholar
• Shapiro , A. 1988 . “Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis,” . International Statistical Review , 56 : 49 – 42 .
   Web of Science ®Google Scholar
• Wang , Y. 1996 . “A Likelihood Ratio Test Against Stochastic Ordering in Several Populations,” . Journal of the Americal Statistical Association , 91 : 1676 – 1683 .
   Web of Science ®Google Scholar
• Wolak , F. A. 1991 . “The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models,” . Econometrica , 59 : 981 – 995 .
   Web of Science ®Google Scholar