ABSTRACT - Some Tests on Exponential Populations.
Abstract Formulation of the Individual Ergodic Theorem
On -optimality of the LR tests
On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions
A quantile goodness-of-fit test applicable to distributions with non-differentiable densities
On Hodges-Lehmann optimality of LR tests
On optimality of the LR tests in the sense of exact slopes. I. General case
On consistency of the MLE
Simultaneous channels decomposable into memoryless components. II
Simultaneous channels decomposable into memoryless components. I
Asymptotic distribution of the likelihood ratio test statistic in the multisample case
On testing hypotheses approximable by cones
On conditional expectations of vector valued variables
A note on the weak convergence of probability measures on
Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions
Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...
On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties
Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification...
The multisample version of the Lepage test
The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of sampled populations. It is shown that its limiting distribution is the chi-square distribution with degrees of freedom. This -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular...
On the two-sided multiparameter control
On testing hypotheses in the generalized Skillings-Mack random blocks setting
The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...
Estimates of the covariance matrix of vectors of u-statistics and confidence regions for vectors of Kendall's tau
Consistent estimators of the asymptotic covariance matrix of vectors of -statistics are used in constructing asymptotic confidence regions for vectors of Kendall’s correlation coefficients corresponding to various pairs of components of a random vector. The regions are products of intervals computed by means of a critical value from multivariate normal distribution. The regularity of the asymptotic covariance matrix of the vector of Kendall’s sample coefficients is proved in the case of sampling...
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