LINEARIZATION VARIANCE ESTIMATORS FOR SURVEY DATA

Abstract

In survey sampling, Taylor linearization is often used to estimate nonlinear finite population parameters such as ratios, regression and correlation coefficients which can be expressed as smooth functions of totals. It is generally applicable to any sampling design, but it can lead to more than one variance estimator that are asymptotically equivalent under repeated sampling. The choice among the variance estimators requires other considerations such as conditional properties of the variance estimators. A new approach to deriving Taylor linearization variance estimators is proposed. This method is based on representing Taylor linearization in terms of partial derivatives with respect to design weights. It leads to variance estimators with good conditional properties and agrees with a jackknife linearization variance estimator when the latter is applicable. We apply the method to a variety ofproblerns, covering general calibration estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. Our approach leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. Extensions to two phase sampling are also presented.