Two-dimensional Kolmogorov-type Goodness-of-fit Tests Based on Characterizations and their Asymptotic Efficiencies

In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for goodness-of-fit testing. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case

New L2-type exponentiality tests

We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L2 distance between V-empirical Laplace transforms of random variables that appear in the characterization. We derive the asymptotic behaviour under the null hypothesis as well as under fixed alternatives. We compare our tests, in terms of the Bahadur efficiency, to the likelihood ratio test, as well as some recent characterization based goodness-of-fit tests for the exponential distribution. We also compare the power of our tests to the power of some recent and classical exponentiality tests. According to both criteria, our tests are shown to be strong and outperform most of their competitors.Peer Reviewe

Some Characterizations of Exponential Distribution Based on Order Statistics

In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved

Asymptotic distribution of certain degenerate V- and U-statistics with estimated parameters

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems

A test for normality and independence based on characteristic function

In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the difference between the product of empirical characteristic functions and some constant. Special attention is given to the case of testing univariate normality in which we derive the test statistic explicitly in terms of Bessel function, and the case of testing bivariate normality and independence. The tests show quality performance in comparison to some popular powerful competitors

Asymptotic distribution of certain degenerate V- and U-statistics with estimated parameters

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems