Asymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a nonnormal one-way ANOVA model
نویسندگان
چکیده
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 percentage points and actual test sizes of this statistic based on the limiting distribution and the asymptotic expansion.
منابع مشابه
Tracking Interval for Doubly Censored Data with Application of Plasma Droplet Spread Samples
Doubly censoring scheme, which includes left as well as right censored observations, is frequently observed in practical studies. In this paper we introduce a new interval say tracking interval for comparing the two rival models when the data are doubly censored. We obtain the asymptotic properties of maximum likelihood estimator under doubly censored data and drive a statistic for testing the ...
متن کاملA New Approximation for the Null Distribution of the Likelihood Ratio Test Statistics for k Outliers in a Normal Sample
Usually when performing a statistical test or estimation procedure, we assume the data are all observations of i.i.d. random variables, often from a normal distribution. Sometimes, however, we notice in a sample one or more observations that stand out from the crowd. These observation(s) are commonly called outlier(s). Outlier tests are more formal procedures which have been developed for detec...
متن کاملTesting Equality of Several Correlation Matrices Prueba de Igualdad de Varias Matrices de Correlación
In this article we show that the Kullback’s statistic for testing equality of several correlation matrices may be considered a modified likelihood ratio statistic when sampling from multivariate normal populations. We derive the asymptotic null distribution of L∗ in series involving independent chisquare variables by expanding L∗ in terms of other random variables and then inverting the expansi...
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 کاملAsymptotic Expansion of Null Distribution of Likelihood Ratio Statistic in Multiparameter Exponential Family to an Arbitrary Order
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 ...
متن کامل