Repeated significance tests based on likelihood ratio statistics

For a specified decision rule, a general class of likelihood ratio based repeated significance tests is considered. An invariance principle for the likelihood ratio statistics is established and incorporated in the study of the asymptotic theory of the proposed tests. For comparing these tests with the conventional likelihood ratio tests, based solely on the target sample size, some Bahadur efficiency results are presented. The theory is then adapted in the study of some multiple comparison procedures     

On the sample size of curtailed tests

Formulas are given for the asymptotic distribution, mean, and variance of m^-1N_m,where NN_m is the random sample size of the curtailed version of a fixed-sample most powerful test based on sample size m. The adequacy of the formulas is numerically investigated in some important applications where exact formulas can also be derived     

Sequential point estimation of the means of u-statistics in finite population sampling

In simple random sampling without replacement from a finite population, sequential point estimators of the means of U-statistics are proposed. The proposed procedure is shown to be asymptotically risk efficient in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185)     

A general robustness property of rank correlations

Rank correlations are shown to be generally robust in the sense that the tests for independence, which they naturally define, have weakly equicontinuous error probabilities. The ordinary sample correlation coefficient is not robust in this respect.     

On minimum distance estimation of location based on the kolmogorov statistic

The asymptotic distribution is derived for the minimum distance estimator of a location parameter based on the Kolmogorov goodness of fit statistic. The distribution is expressed in terms of the distribution of a functional of a Brownian bridge. An upper bound is obtained for the length of the confidence interval based on the Kolmogorov statistic. A simulation study with sample sizes 10 and 20 compares the length of the interval based on the Kolmogorov statistic to the length of the interval based on the maximum likelihood estimator. Another simulation shows the effect of model misspecification on the coverage probabilities of the interval based on the Kolmogorov statistic.     

A general procedure for deriving distributions

A general procedure for deriving the exact and asymptotic distributions of a certain class of test statistics in multivariate analysis is proposed. The method is based on an asymptotic expansion of gamma ratios in terms of generalized Bernoulli polynomials. The exact and asymptotic results are obtained and the method is illustrated in the problem of testing linear hypotheses in the multinomial case. In this problem the method yields Box's (1949) expansion as a special case.     

Tests of homogeneity of intercepts after a preliminary test

For the multl-sample regression model , the problem of testing equality of intercepts following a preliminarytest on the equality o f slopes is considered. The t e s t s are based on the conventional least squares estimators (without necessarily assuming the normality of the underlying error distributions ) , and the impact of a

preliminary test on the asymptotic size and power of the final test is studied.     

On the uniformly asymptotic normality of frequency polygons for ψ-mixing samples

The uniformly asymptotical normality of frequency polygons for ψ-mixing samples is investigated under the given conditions. Moreover, the corresponding rate of convergence is also derived, which is nearly O(n^{? 1/6}) for the given assumptions.     

Estimation of the linear EV model with censored data

In this paper, a censored linear errors-in-variables model is investigated. The asymptotic normality of the unknown parameter's estimator is obtained. Two empirical log-likelihood ratio statistics for the unknown parameter in the model are suggested. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameter of interest. Finite sample performance of the proposed method is illustrated in a simulation study.     

Comparison of two weibull distributions under random censoring

The two-sample problem for comparing Weibull scale parameters is studied for randomly censored data. Three different test statistics are considered and their asymptotic properties are established under a sequence of local alternatives, It is shown that both the test statistic based on the mlefs (maximum likelihood estimators) and the likelihood ratio test are asymptotically optimum. The third statistic based only on the number of failures is not, Asymptotic relative efficiency of this statistic is obtained and its numerical values are computed for uniform and Weibull censoring, Effects of uniform random censoring on the censoring level of the experiment are illus¬trated, A direct proof for the joint asymptotic normality of the mlefs of the shape and the scale parameters is also given