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On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables

Navaei, Leader (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62P30.In this paper by using theory of large deviation techniques (LDT), the problem of hypotheses testing for three random variables having different distributions from three possible distributions is solved. Hypotheses identification for two objects having different distributions from two given probability distributions was examined by Ahlswewde and Haroutunian. We noticed Sanov's theorem and its applications in hypotheses testing.

On strong laws for generalized L-statistics with dependent data

David Gilat, Roelof Helmers (1997)

Commentationes Mathematicae Universitatis Carolinae

It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).

On testing hypotheses in the generalized Skillings-Mack random blocks setting

František Rublík (2011)

Kybernetika

The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...

On testing of general random closed set model hypothesis

Tomáš Mrkvička (2009)

Kybernetika

A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set Ξ ⊆ ℝ d with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the ε -parallel sets to Ξ . The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation...

On testing variance components in unbalanced mixed linear model

Lýdia Širková, Viktor Witkovský (2001)

Applications of Mathematics

The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.

On the adaptive wavelet estimation of a multidimensional regression function under α -mixing dependence: Beyond the standard assumptions on the noise

Christophe Chesneau (2013)

Commentationes Mathematicae Universitatis Carolinae

We investigate the estimation of a multidimensional regression function f from n observations of an α -mixing process ( Y , X ) , where Y = f ( X ) + ξ , X represents the design and ξ the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of f in its construction) or it is supposed that ξ is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....

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