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## Prace Naukowe / Akademia Ekonomiczna w Katowicach

2003 | 226
Tytuł artykułu

### Some Contributions to Multivariate Methods in Survey Sampling

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EN
Abstrakty
EN
The book can be treated as a set of contributions to the estimation of a vector of the averages of variables in a finite population. The methods presented are not only a simple generalisation of the well known problems on a multidimensional case but a lot of them can be treated as original ones. Particularly, several sampling strategies dependent on auxiliary variables arc proposed. The problems of optimising a sample size are considered in detail for stratified and two-stage sampling designs in the case when more than one average in a population is estimated. The well known discrimination and clustering methods and their modifications are used for optimal stratification or clustering of a fixed population. Solutions obtained here can be useful in optimisation of estimation on the basis of a double sample. The book presents some contributions to interpretations of the following measures of accuracy of vector estimators: the generalised variance, the mean radius and spectral radius defined as a determinant, the trace and the maximal eigenvalue of the variance-covariance matrix, respectively. Some definitions and theorems, known in a one-dimensional case are extended to the vector estimation case. They let us compare the accuracy of vector estimators. The properties of sampling designs and sampling schemes depend on the parameters of auxiliary variables like the sample generalised variance, the squared difference between the sample mean and the population mean are considered. The approximate expressions of the variance of the Horovitz-Thompson estimator of the mean value are derived for these sampling designs. The unbiased estimators of the generalised variance are found in the cases when the simple sample is drawn with as well as without replacement. (fragment of the original abstract)
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226
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• The Karol Adamiecki University of Economics in Katowice, Poland
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