arXiv subjects
Publications and source records attributed to Marko Obradović.
We prove a novel characterization of the exponential distribution via a linear combination of order statistics. The theorem established herein generalizes the previous characterization theorem given in Milošević and Obradović (2016a). The proof relies on properties of Stirling numbers of the second kind, which are derived for this purpose and may be of independent interest.
This paper presents a comprehensive study of nonparametric estimation techniques on the circle using Fejér polynomials, which are analogues of Bernstein polynomials for periodic functions. Building upon Fejér's uniform approximation theorem, the paper introduces circular density and distribution function estimators based on Fejér kernels. It establishes their theoretical properties, including uniform strong consistency and asymptotic expansions. Since the estimation of the distribution function on the circle depends on the choice of the origin, we propose a data-dependent method to address this issue. The proposed methods are extended to account for measurement errors by incorporating classical and Berkson error models, adjusting the Fejér estimator to mitigate their effects. Simulation studies analyze the finite-sample performance of these estimators under various scenarios, including mixtures of circular distributions and measurement error models. An application to rainfall data demonstrates the practical application of the proposed estimators, demonstrating their robustness and effectiveness in the presence of rounding-induced Berkson errors.
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.
We study the Bahadur efficiency of several weighted L2--type goodness--of--fit tests based on the empirical characteristic function. The methods considered are for normality and exponentiality testing, and for testing goodness--of--fit to the logistic distribution. Our results are helpful in deciding which specific test a potential practitioner should apply. For the celebrated BHEP and energy tests for normality we obtain novel efficiency results, with some of them in the multivariate case, while in the case of the logistic distribution this is the first time that efficiencies are computed for any composite goodness--of--fit test.
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.
In this paper some well-known tests based on empirical distribution functions (EDF) with estimated parameters for testing composite normality hypothesis are revisited, and some new results on asymptotic properties are provided. In particular, the approximate Bahadur slopes are obtained -- in the case of close alternatives -- for the EDF-based tests as well as the likelihood ratio test. The local approximate efficiencies are calculated for several close alternatives. The obtained results could serve as a benchmark for evaluation of the quality of recent and future normality tests.
We present new consistent goodness-of-fit tests for exponential distribution, based on the Desu characterization. The test statistics represent the weighted $L^2$ and $L^{\infty}$ distances between appropriate V-empirical Laplace transforms of random variables that appear in the characterization. In addition, we perform an extensive comparison of Bahadur efficiencies of different recent and classical exponentiality tests. We also present the empirical powers of new tests.
We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on Puri-Rubin characterization. For the construction of test statistics we employ weighted $L^2$ distance between $V$-empirical Laplace transforms of random variables that appear in the characterization. The resulting test statistics are degenerate V-statistics with estimated parameters. 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 powers of our tests to the powers of some recent and classical exponentiality tests. In both criteria, our tests are shown to be strong and outperform most of their competitors.
In this paper, some recent and classical tests of symmetry are modified for the case of an unknown center. The unknown center is estimated with its $α$-trimmed mean estimator. The asymptotic behavior of the new tests is explored. The local approximate Bahadur efficiency is used to compare the tests to each other as well as to some other tests.
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.
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.
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
In this paper we present a new characterization of Pareto distribution and consider goodness of fit tests based on it. We provide an integral and Kolmogorov- Smirnov type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes we compare the power of those tests with some common goodness of fit tests.