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A note on control of the false discovery proportion

Marcin Dudziński, Konrad Furmańczyk (2009)

Applicationes Mathematicae

We consider the problem of simultaneous testing of a finite number of null hypotheses H i , i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned with...

A procedure for ε-comparison of means of two normal distributions

Stanisław Jaworski, Wojciech Zieliński (2004)

Applicationes Mathematicae

For two normal distributions N(μ₁,σ²) and N(μ₂,σ²) the problem is to decide whether |μ₁-μ₂|≤ ε for a given ε. Two decision rules are given: maximin and bayesian for σ² known and unknown.

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

František Rublík (2011)


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 the Behrens-Fisher distribution and its generalization to the pairwise comparisons

Viktor Witkovský (2002)

Discussiones Mathematicae Probability and Statistics

Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals....

Optimal stopping of a risk process

Elżbieta Ferenstein, Andrzej Sierociński (1997)

Applicationes Mathematicae

Optimal stopping time problems for a risk process U t = u + c t - n = 0 N ( t ) X n where the number N(t) of losses up to time t is a general renewal process and the sequence of X i ’s represents successive losses are studied. N(t) and X i ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process.

Thomas L. Saaty (2008)


According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...

Selection in parametric models via some stepdown procedures

Konrad Furmańczyk (2014)

Applicationes Mathematicae

The paper considers the problem of consistent variable selection in parametic models with the use of stepdown multiple hypothesis procedures. Our approach completes the results of Bunea et al. [J. Statist. Plann. Inference 136 (2006)]. A simulation study supports the results obtained.

The multisample version of the Lepage test

František Rublík (2005)


The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of k > 1 sampled populations. It is shown that its limiting distribution is the chi-square distribution with 2 ( k - 1 ) degrees of freedom. This k -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular...

Using the one-versus-rest strategy with samples balancing to improve pairwise coupling classification

Wiesław Chmielnicki, Katarzyna Stąpor (2016)

International Journal of Applied Mathematics and Computer Science

The simplest classification task is to divide a set of objects into two classes, but most of the problems we find in real life applications are multi-class. There are many methods of decomposing such a task into a set of smaller classification problems involving two classes only. Among the methods, pairwise coupling proposed by Hastie and Tibshirani (1998) is one of the best known. Its principle is to separate each pair of classes ignoring the remaining ones. Then all objects are tested against...

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