Multivariate likelihood ratio order of order statistics conditioned on both the right tail and the left tail are built. These results strengthen and generalize those conclusions in terms of the univariate likelihood r...Multivariate likelihood ratio order of order statistics conditioned on both the right tail and the left tail are built. These results strengthen and generalize those conclusions in terms of the univariate likelihood ratio order by Khaledi and Shaked （2007）, Li and Zhao （2006）, Hu, et al. （2006）, and Hu, Jin, and Khaledi （2007）.展开更多
Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, w...Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i’s are to be of interest and P0i’s are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as展开更多
Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boun...Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.展开更多
基金This research is supported by the National Natural Science Foundations of China under Grant No. 10771090. Authors thank Professor Xiaohu Li for providing us insightful instruction and his encouraging comments on this manuscript.
文摘Multivariate likelihood ratio order of order statistics conditioned on both the right tail and the left tail are built. These results strengthen and generalize those conclusions in terms of the univariate likelihood ratio order by Khaledi and Shaked （2007）, Li and Zhao （2006）, Hu, et al. （2006）, and Hu, Jin, and Khaledi （2007）.
文摘Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i’s are to be of interest and P0i’s are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as
文摘Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.
基金Supported by the NNSF of China(Grant No.:10171093)the National 973 Fundamental Research Program on Financial Engineering(Grant No:G1998030418)the Doctoral Program Foundation of Institute of High Education.
