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### On equivalence problem in linear regression models. I. BLUE of the mean value

Aplikace matematiky

There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.

### On equivalence problem in linear regression models. II. Unbiased estimation of the covariance matrix scalar factor

Aplikace matematiky

There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.

### Minimum mean square error estimation

Aplikace matematiky

In many cases we can consider the regression parameters as realizations of a random variable. In these situations the minimum mean square error estimator seems to be useful and important. The explicit form of this estimator is given in the case that both the covariance matrices of the random parameters and those of the error vector are singular.

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

### Estimation in a special structure of the linear model

Mathematica Slovaca

### Covariance matrix elements estimation: special linear model without and with repeated measurement

Mathematica Slovaca

### Linear-quadratic estimators in a special structure of the linear model

Applications of Mathematics

The paper deals with the linear model with uncorrelated observations. The dispersions of the values observed are linear-quadratic functions of the unknown parameters of the mean (measurements by devices of a given class of precision). Investigated are the locally best linear-quadratic unbiased estimators as improvements of locally best linear unbiased estimators in the case that the design matrix has none, one or two linearly dependent rows.

### Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model

Applications of Mathematics

The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.

### Bad luck in quadratic improvement of the linear estimator in a special linear model

Applications of Mathematics

The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.

### Book Reviews

Mathematica Slovaca

### Linear model with variances depending on the mean value

Mathematica Slovaca

### On the generalization of the STER distribution applied to generalized hypergeometric parents

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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

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

Kybernetika

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

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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