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### O teorii strategických her

Pokroky matematiky, fyziky a astronomie

### [On the scientific symposium of the Charles University and University of Hamburg, Prague, 1982]

Acta Universitatis Carolinae. Mathematica et Physica

### Dependent random variables with a given marginal distribution

Acta Universitatis Carolinae. Mathematica et Physica

### An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Applications of Mathematics

Let ${𝕖}_{t}={\left({e}_{t1},\cdots ,{e}_{tp}\right)}^{\text{'}}$ be a $p$-dimensional nonnegative strict white noise with finite second moments. Let ${h}_{ij}\left(x\right)$ be nondecreasing functions from $\left[0,\infty \right)$ onto $\left[0,\infty \right)$ such that ${h}_{ij}\left(x\right)\le x$ for $i,j=1,\cdots ,p$. Let $𝕌=\left({u}_{ij}\right)$ be a $p×p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process ${𝕏}_{t}={\left({X}_{t1},\cdots ,{X}_{tp}\right)}^{\text{'}}$ by ${X}_{tj}={u}_{j1}{h}_{1j}\left({X}_{t-1,1}\right)+\cdots +{u}_{jp}{h}_{pj}\left({X}_{t-1,p}\right)+{e}_{tj}$ for $j=1,\cdots ,p$. A method for estimating $𝕌$ from a realization ${𝕏}_{1},\cdots ,{𝕏}_{n}$ is proposed. It is proved that the estimators are strongly consistent.

### The efficiency of estimates in stationary autoregressive series

Aplikace matematiky

### Statistical analysis of periodic autoregression

Aplikace matematiky

Methods for estimating parameters and testing hypotheses in a periodic autoregression are investigated in the paper. The parameters of the model are supposed to be random variables with a vague prior density. The innovation process can have either constant or periodically changing variances. Theoretical results are demonstrated on two simulated series and on two sets of real data.

### Periodic autoregression with exogenous variables and periodic variances

Aplikace matematiky

The periodic autoregressive process with non-vanishing mean and with exogenous variables is investigated in the paper. It is assumed that the model has also periodic variances. The statistical analysis is based on the Bayes approach with a vague prior density. Estimators of the parameters and asymptotic tests of hypotheses are derived.

### On multiple periodic autoregression

Aplikace matematiky

The model of periodic autoregression is generalized to the multivariate case. The autoregressive matrices are periodic functions of time. The mean value of the process can be a non-vanishing periodic sequence of vectors. Estimators of parameters and tests of statistical hypotheses are based on the Bayes approach. Two main versions of the model are investigated, one with constant variance matrices and the other with periodic variance matrices of the innovation process.

### K šedesátinám Prof. Ing. Františka Fabiana, CSc.

Aplikace matematiky

### K šedesátinám doc. RNDr. Václava Dupače, DrSc.

Časopis pro pěstování matematiky

### On non-nested regression models

Commentationes Mathematicae Universitatis Carolinae

A generalization of a test for non-nested models in linear regression is derived for the case when there are several regression models with more regressors.

### On multiple normal probabilities of rectangles

Aplikace matematiky

### The most significant interaction in a contingency table

Aplikace matematiky

### On the Bayes approach in general multiple autoregressive series

Aplikace matematiky

### The Bayes approach in multiple autoregressive series

Aplikace matematiky

### Iterative solution of the best linear extrapolation problem in multidimensional stationary random sequences

Aplikace matematiky

An iterative method for linear extrapolation of twodimensional random sequences is derived. Steps of this procedure are based (i) on Jaglom’s method, (ii) on Hájek’s method. A numerical example is given in the both cases. Finally the iterative method is generalized for the $n$ - dimensional case.

### On interactions in contingency tables

Aplikace matematiky

### On evaluation of some two-dimensional normal probabilities

Aplikace matematiky

### On simulation of multidimensional random sequences

Acta Universitatis Carolinae. Mathematica et Physica

Kybernetika

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