Statistical Inference for Simple Tree Order in the Means of Stochastic Order on Stratified Contingency Tables
Statistical Inference for Simple Tree Order in the Means of Stochastic Order on Stratified Contingency Tables
摘要
In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.
In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.
作者
YAN Guoyi1,2, CHEN Jingjing3 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
2. School of Sciences, Wuhan Institute of Technology, Wuhan 430074, Hubei, China
3. School of Sciences, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China
基金
Supported by the National Natural Science Foundation of China (10771163)
参考文献12
-
1Barlow R E, Bartholomew D J, Bremner J M, et al. Statistical Inference under Order Restrictions[M]. New York: Wiley Press, 1972.
-
2Grove D M. A testing of independence against a class of ordered alternatives in a 2× c contingency table[J]. Journal of the American Statistical Association, 1980, 75: 454-459.
-
3Bhattacharya B, Dykstra R L. Statisticalinference for stochastic ordering[M]//Shaked M, Shanthikumar J G. Stochastic Orders and Their Applications. Boston:Academic Press, 1994.
-
4Bartholomew D J. A test for homogeneity of means under restricted alternative[J]. Journal of the Royal Statistical Society Ser B, 1961, 23:239-281.
-
5Tang D I, Lin S P. An approximate likelihood ratio test for comparing several treatments to a control[J]. Journal of the American Statistical Association, 1997, 92:1155-1162.
-
6Chuang-Stein C, Agresti A. A review of tests for detecting a monotone dose-response relationship with ordinal response data[J]. Statistics in Medicine, 1997, 16:2599-2618.
-
7Stoyan D. Comparison Methods for Queues and other Stochastic Models[M]. New York: Wiley Press, 1983.
-
8Wang Y. A Likelihood ratio test against stochastic ordering in several populations [J]. Journal of the American Statistical Association, 1996, 91: 1676-1683.
-
9Dykstra R, Kochar S, Robertson T. Statistical inference for uniform stochastic ordering in several populations[J]. Annals of Statistics, 1991, 19: 870-888.
-
10Liu X, Wang J. Testing for increasing convex order in several populations[J]. Annals of the Institute of Statistical Mathematics, 2003, 1: 121-136.
-
1贾国柱.多元回归分析的编程及使用说明[J].新疆钢铁,1989(1):41-50.
-
2叶慈南.STATISTICAL INFERENCE PROCEDURE FOR A BIVARIATE EXPONENTIAL DISTRIBUTION[J].Acta Mathematicae Applicatae Sinica,1994,10(1):75-89.
-
3WANG Dongqian(Department of Statistics and Operations Research Royal Melbourne Institute of Technology,Melbourne,Vic 3001, Australia)Nancy B. WU(Ballarat Grammar School 201 Forest Street, Wendouree, Vic 3355, Australia).METHODS OF ESTIMATION FOR QUASI-INDEPENDENCE IN CONTINGENCY TABLES[J].Systems Science and Mathematical Sciences,1999,12(4):292-298.
-
4ZHANG Shu-lin,WEI Zheng-hong,BI Qiu-xiang.A Linear Immigration-Birth-Death Model and Its Statistical Inference[J].Chinese Quarterly Journal of Mathematics,2014,29(3):356-362.
-
5WU Shanshan MIAO Baiqi (Department of Statistics and Finance, University of Science & Technology of China, Hefei 230026, China).STATISTICAL INFERENCE FOR CONTAMINATION DISTRIBUTION[J].Journal of Systems Science & Complexity,2001,14(3):311-321. 被引量:1
-
6DONG Jianping(Department of Mathematical Sciences, Michigan Technological University,Houghton, MI 49931, U.S.A.).ON AVOIDING ASSOCIATION PARADOXES INCONTINGENCY TABLES[J].Systems Science and Mathematical Sciences,1998,11(3):272-279.
-
7Abdalroof M S,Zhao Zhi-wen,Wang De-hui.Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Type-I Interval Censored Sample[J].Communications in Mathematical Research,2015,31(2):108-118. 被引量:1
-
8Abdalroof M.S.,Zhao Zhi-wen,Wang De-hui.Statistical Inference for the Parameter of Pareto Distribution Based on Progressively Type-I Interval Censored Sample[J].Communications in Mathematical Research,2014,30(4):345-357.
-
9Bing HE,Jin-hong YOU,Min CHEN.Statistical Inference on Seemingly Unrelated Single-Index Regression Models[J].Acta Mathematicae Applicatae Sinica,2016,32(4):945-956.
-
10ZHAO Lincheng ZHANG Hong(University of Science and Technology of China, Hefei, Anhui 230026. China).MODEL SELECTION FOR LOG-LINEAR MODELS OF CONTINGENCY TABLES[J].Journal of Systems Science & Complexity,2003,16(2):249-259. 被引量:1