This paper proposes a new goodness-of-fit test for normality based on the L~ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distribute...This paper proposes a new goodness-of-fit test for normality based on the L~ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval （0, 1） under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.展开更多
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
基金supported by the National Natural Science Foundation of China under Grant Nos.11201005 and 11071015the Natural Science Foundation of Anhui Province under Grant Nos.1308085QA13 and 1208085MA11the Key Project of Anhui Education Committee under Grant Nos.KJ2012A135 and 2012SQRL028ZD
文摘This paper proposes a new goodness-of-fit test for normality based on the L~ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval （0, 1） under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.
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.
