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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....

Modified minimax quadratic estimation of variance components

Viktor Witkovský — 1998


The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

Computing the distribution of a linear combination of inverted gamma variables

Viktor Witkovský — 2001


A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized p -values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear...

A Note on Computing Extreme Tail Probabilities of the Noncentral t -Distribution with Large Noncentrality Parameter

Viktor Witkovský — 2013

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The noncentral t -distribution is a generalization of the Student’s t -distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral t -distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral t -distribution, even for large values of the noncentrality...

Estimation of variance components in mixed linear models

Júlia VolaufováViktor Witkovský — 1992

Applications of Mathematics

The MINQUE of the linear function ' ϑ of the unknown variance-components parameter ϑ in mixed linear model under linear restrictions of the type 𝐑 ϑ = c is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions ϑ 1 = k ϑ 2 , where k 0 , is given.

Note on a Calibration Problem: Selected Results and Extensions of Professor Kubáček’s

Gejza WimmerViktor Witkovský — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Professor Lubomír Kubáček has provided exceptional contributions to mathematical statistics and its applications. Because of his excellent knowledge in mathematical statistics as well as in the different fields of natural and especially technical sciences, he contributed to solution of a large number of real world problems. The continuation of Professor Kubáček’s scientific work and his scientific school is demonstrated by the results of his numerous students. Here we present just one illustration...

Linear comparative calibration with correlated measurements

Gejza WimmerViktor Witkovský — 2007


The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the...

On small sample inference for common mean in heteroscedastic one-way model

Viktor WitkovskýAlexander SavinGejza Wimmer — 2003

Discussiones Mathematicae Probability and Statistics

In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward...

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