Asymptotic Expansion of Null Distribution of Likelihood Ratio Statistic in Multiparameter Exponential Family to an Arbitrary Order
نویسندگان
چکیده
Consider likelihood ratio test of a simple null hypothesis in a multiparameter exponential family. We study the asymptotic expansion of the null distribution of log likelihood ratio statistic to an arbitrary order. Bartlett correctability of the O(n ) term is well known. We show that higher order terms exhibit a similar simplicity. Moreover we give a combinatorially explicit expression for all terms of the asymptotic expansion of the characteristic function of log likelihood ratio statistic.
منابع مشابه
Asymptotic Expansions of Thelikelihood Ratio Test Statistic
SUMMARY. Likelihood ratio tests are used to test ordered hypotheses involving the parameters of k independent samples from an exponential family. For the test of constancy of the parameters versus an ordered alternative, the likelihood ratio test statistic is asymptotically distributed as a mixture of k chi-squared distributions under the null hypothesis. This paper derives an asymptotic expans...
متن کاملAsymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a nonnormal one-way ANOVA model
This paper is concerned with the null distribution of the likelihood ratio statistic for testing the equality of variances of q nonnormal populations. It is known that the null distribution of this statistic converges to w q 1 under normality. We extend this result by obtaining an asymptotic expansion under general conditions. Numerical accuracies are studied for some approximations of the perc...
متن کاملIntroducing a New Lifetime Distribution of Power Series Distribution of the Family Gampertz
In this Paper, We propose a new three-parameter lifetime of Power Series distributions of the Family Gampertz with decreasing, increasing, increasing-decreasing and unimodal Shape failure rate. The distribution is a Compound version of of the Gampertz and Zero-truncated Possion distributions, called the Gampertz-Possion distribution (GPD). The density function, the hazard rate function, a gener...
متن کاملAccurate Inference for the Mean of the Poisson-Exponential Distribution
Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...
متن کاملThe local power of the gradient test
The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n−1/2, n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all fo...
متن کامل