Order Restricted Statistical Tests on Multinomial and Poisson Parameters: The Starshaped Restriction
作者： Richard L. Dykstra , Tim Robertson
关键词: Multinomial distribution 、 Statistical hypothesis testing 、 Combinatorics 、 Asymptotic distribution 、 Null distribution 、 Multinomial test 、 Poisson distribution 、 Test statistic 、 Applied mathematics 、 Chi-square test 、 Mathematics
摘要: Abstract : Likelihood ratio statistics for (i) testing the homogeneity of a collection multinomial parameters against alternative which accounts restriction that those are starshaped (cf. Shaked, Ann. Statist. (1979)), and (ii) null hypothesis this parameter vector is considered. For both tests asymptotic distribution test statistic under version chi-bar-square distribution. Analogous on Poisson means also found to have distributions. (Author)
sci-hub.se 参考文章(8)
D. J. BARTHOLOMEW, A TEST OF HOMOGENEITY FOR ORDERED ALTERNATIVES. II Biometrika. ,vol. 46, pp. 328- 335 ,(1959) , 10.1093/BIOMET/46.3-4.328
Tim Robertson, F. T. Wright, On Measuring the Conformity of a Parameter Set to a Trend, with Applications Annals of Statistics. ,vol. 10, pp. 1234- 1245 ,(1982) , 10.1214/AOS/1176345988
Tim Robertson, Edward J. Wegman, Likelihood Ratio Tests for Order Restrictions in Exponential Families Annals of Statistics. ,vol. 6, pp. 485- 505 ,(1978) , 10.1214/AOS/1176344195
Richard L. Dykstra, Tim Robertson, On Testing Monotone Tendencies Journal of the American Statistical Association. ,vol. 78, pp. 342- 350 ,(1983) , 10.1080/01621459.1983.10477976
Tim Robertson, Testing for and against an Order Restriction on Multinomial Parameters Journal of the American Statistical Association. ,vol. 73, pp. 197- 202 ,(1978) , 10.1080/01621459.1978.10480028
Moshe Shaked, Estimation of Starshaped Sequences of Poisson and Normal Means Annals of Statistics. ,vol. 7, pp. 729- 741 ,(1979) , 10.1214/AOS/1176344724
J. D. Kalbfleisch, Statistical Inference Under Order Restrictions Technometrics. ,vol. 17, pp. 139- 140 ,(1975) , 10.1080/00401706.1975.10489288
Patrick Billingsley, Convergence of Probability Measures ,(1968)