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Class of Estimators of Mean and Variance Using Auxiliary Information when Correlation Coefficient is also Known
Author(s) -
Srivastava S. K.,
Jhajj H. Singh
Publication year - 1983
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.19830250409
Subject(s) - mathematics , estimator , statistics , mean squared error , variance (accounting) , correlation coefficient , sample size determination , population mean , population , correlation , efficiency , demography , accounting , sociology , business , geometry
For estimating the mean of a finite population using information on an auxiliary variable, a class of estimators which also uses the value of the correlation coefficient between the two variables which is assumed known, is defined. Expression for its asymptotic mean squared error and its minimum value is obtained. An expression by which the minimum mean squared error of this class is smaller than those which use only the sample mean and the sample variance of the auxiliary variable is obtained. A similar class of estimators is considered for the estimation of the population variance. The gain in efficiency is illustrated for six populations considered in literature.