Theory & Methods: Calibration of the estimators of variance

Abstract

This investigation suggests new techniques to calibrate estimators of variance. Estimators of the variance of simple mean, ratio and regression estimators under different sampling schemes are shown to be special cases of the proposed calibration techniques. The approach has more practical use due to recent advances in programming techniques and computational speed. An empirical study has been carried out to address the properties of these proposed strategies.

Calibration approach estimators in stratified sampling

“…Deville and Sa¨rndal (1992) first presented calibration estimators in survey sample and calibration estimation has been studied by many survey statisticians. A few key references are Dupont (1995), Hidiroglou and Sa¨rndal (1998), Singh et al (1998Singh et al ( , 1999, Singh (2001), Sitter and Wu (2002), and Tracy et al (2003). Wu and Sitter (2001) and Sitter and Wu (2002) generalize the calibration procedure by means of model calibrations and extend a pseudo-empirical likelihood method to obtain efficient estimator of quadratic and other second-order finite population functions.…”

A Monte Carlo comparison of some variance estimators of the Horvitz–Thompson estimator

“…Inserting Equation (8) in (10), we get This estimator is so intuitively plausible, following directly from Royall's approach of replacing a population sum by the sample sum plus a model-based estimator of the non-sample sum. (6), for any design p,…”

“…Singh et al [8] proposed a high-level calibration approach for variance estimation. To estimate V YGY their calibration estimators are…”

“…Recently, Singh et al [8] obtained a calibration estimator by adjusting V YGY in such a manner that it reduces the variance through the use of auxiliary information. A major disadvantage of their estimator is that it is not useful for PPS sampling (under which π -estimator is optimal).…”

Model-Assisted Higher-Order Calibration of Estimators of Variance

“…These quantities can be determined if information about the auxiliary variable is available for each unit in the population; for example, the turnover per establishment, as recorded in a census or in administrative records. Das & Tripathi (1978), Srivastava & Jhajj (1981), Garcia & Cebrian (1996), Shah & Patel (1996) and Singh et al (1999) have also considered estimation of the variance of various estimators of the population total when the auxiliary variable variance is known. Theberge (1999) has also considered a calibration-based approach to variance estimation.…”