In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-value...In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.展开更多
This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modifi...This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10271013, 10771015)
文摘In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.
基金the National Natural Science Foundation of China (Grant No. 10661003)the Natural Science Foundation of Guangxi (Grant No. 0728092) SRF for ROCS, SEM (Grant No. [2004]527)
文摘This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.
