170 research outputs found
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
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