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Simos G. Meintanis (2007)
Kybernetika
A sub-exponential Weibull random variable may be expressed as a quotient of a unit exponential to an independent strictly positive stable random variable. Based on this property, we propose a test for exponentiality which is consistent against Weibull and Gamma distributions with shape parameter less than unity. A comparison with other procedures is also included.
Jamal-Dime Chergui (1996)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
I.A. Ahmad, S.G. Kochar (1990)
Metrika
F Czekała (1991)
Applicationes Mathematicae
Luc Devroye (1989)
Annales de l'I.H.P. Probabilités et statistiques
Brahim Ouhbi, Ali Boudi, Mohamed Tkiouat (2007)
RAIRO - Operations Research
In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
Abdelkader Mokkadem, Mariane Pelletier (2003)
ESAIM: Probability and Statistics
Let be the mode of a probability density and its kernel estimator. In the case is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for . Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the norms, , of ....
Abdelkader Mokkadem, Mariane Pelletier (2010)
ESAIM: Probability and Statistics
Let θ be the mode of a probability density and θn its kernel estimator. In the case θ is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for θn - θ. Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence θn - θ suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the...
Jean-Marc Azaïs, Élisabeth Gassiat, Cécile Mercadier (2009)
ESAIM: Probability and Statistics
This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations...
Griffin, Philip S. (2002)
Electronic Communications in Probability [electronic only]
Simos G. Meintanis, Gilles Stupfler (2015)
Kybernetika
We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.
Jana Jurečková (1983)
Commentationes Mathematicae Universitatis Carolinae
Axel Tenbusch (1994)
Metrika
Eugenia Stoimenova (2007)
Applications of Mathematics
Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s -test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics.
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