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Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality

Christoph Aistleitner, Josef Dick (2015)

Acta Arithmetica

We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure...

GTES : une méthode de simulation par jeux et apprentissage pour l'analyse des systèmes d'acteurs

Y. Caseau (2009)

RAIRO - Operations Research

Cet article décrit une approche de la modélisation d'un système d'acteurs, particulièrement adaptée à la modélisation des entreprises, fondée sur la théorie des jeux [11] et sur l'optimisation par apprentissage du comportement de ces acteurs. Cette méthode repose sur la combinaison de trois techniques : la simulation par échantillonnage (Monte-Carlo), la théorie des jeux pour ce qui concerne la recherche d'équilibre entre les stratégies, et les méthodes heuristiques d'optimisation locale,...

How powerful are data driven score tests for uniformity

Tadeusz Inglot, Alicja Janic (2009)

Applicationes Mathematicae

We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...

Improvement of Fisher's test of periodicity

Tomáš Cipra (1983)

Aplikace matematiky

Fisher's test of periodicity in time series and Siegel's version of this test for compound periodicities are investigated in the paper. An improvement increasing the power of the test is suggested and demonstrated by means of numerical simulations.

Inference in linear models with inequality constrained parameters

Henning Knautz (2000)

Discussiones Mathematicae Probability and Statistics

In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and...

Inference on overlap coefficients under the Weibull distribution : equal shape parameter

Obaid Al-Saidy, Hani M. Samawi, Mohammad F. Al-Saleh (2005)

ESAIM: Probability and Statistics

In this paper we consider three measures of overlap, namely Matusia’s measure ρ , Morisita’s measure λ and Weitzman’s measure Δ . These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

Inference on overlap coefficients under the Weibull distribution: Equal shape parameter

Obaid Al-Saidy, Hani M. Samawi, Mohammad F. Al-Saleh (2010)

ESAIM: Probability and Statistics

In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure Δ. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

L p - and S p , q r B -discrepancy of (order 2) digital nets

Lev Markhasin (2015)

Acta Arithmetica

Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the L p -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...

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