Estimation of quadratic finite, Population functions using  calibration

Dalius  Pumputis; Andrius  Čiginas

Estimation of quadratic finite, Population functions using calibration

Dalius Pumputis Lithuanian University of Educational Sciences, Vilnius, Lithuania , Andrius Čiginas Vilnius University, Vilnius, Lithuania Statistics in Transition new series, vol. 12, 2011, 2, pages: 309-330 Published online: 3 October 2011

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ABSTRACT

Since the quadratic finite population functions can be expressed as totals over a synthetic population consisting of some ordered pairs of elements of the initial population, the traditional and penalized calibration technique is used to derive some calibrated estimators of the quadratic finite population functions. A linear combination of estimators discussed is considered as well. A comparison of approximate variances of the calibrated estimators is also presented. A simulation study is performed to analyze the empirical properties of the calibrated estimators of the finite population variance and covariance which appear as special cases of the quadratic functions. It is shown also how the calibrated estimators of the population covariance (variance) can be applied in regression estimation of the finite population total.

KEYWORDS

calibrated estimator; penalized calibration; auxiliary variables; approximate variance.

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