On Estimation of Population Averages on the Basis of Cluster Sample
Clustering methods are applied to improving precision of estimation of means in a fixed and finite population. The particular case of estimation of population means on the basis of sample drawn from a population partitioned into strata by means of clustering algorithms is considered by Huisman (2000) and Wywiał (1995, 1998, 2001). Here an estimator from cluster sample of a vector of population averages is considered. The accuracy of the estimator increases when the degree of the within-cluster spread increases. The precision of the vector estimator is compared with precision of simple sample means. The problem is finding such partition of a population into mutually disjoint clusters that the vector estimator from the cluster sample is more precise estimator of the population averages than the vector of simple sample means. Some clustering algorithm is proposed.
KeywordsCluster Algorithm Vector Variable Simple Sample Vector Estimator Final Partition
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- COCHRAN W.G. (1963), Sampling Techniques, John Wiley, New York.Google Scholar
- FRIEDMAN J. H., RUBIN J. (1967), On some invariant criteria for grouping data. Journal of the American Statistical Association no. 62.Google Scholar
- HUISMAN M. (2000), Post-stratification to correct fornonresponse: classification of ZIP code areas. In: Proc. in Computational Statistics 1.4th Symp. held in Utrecht, The Netherlands, Ed. J.G. Bethlehem and P.G.M. van der Huijden. Physica-Verlag, Heidelberg, New York.Google Scholar
- MACQUEEN J. P. (1967), Some methods for classification and analysis of multivariate observations. In: Proc. of the 5th Berkeley Symp. on Mathematical Statistics and Probability, Berkeley.Google Scholar
- WYWIAL J. (1995), On optimal stratification of population on the basis of auxiliary variables. Statistics in Transition vol. 2, 831–837.Google Scholar
- WYWIAL J. (1998), Estimation of population average on the basis of strata formed by means of discrimination functions. Statistics in Transition vol. 3, 903–912.Google Scholar
- WYWIAL J. (2001), Estimation of population averages on the basis of a vector of cluster means. Paper presented at the Conf. Multivariate Statistical Analysis, Lodi, Department of Statistical Methods, University of Lodi.Google Scholar