Estimating a Population Total Using an Area Frame

Abstract

Land segments form the sampling frame in a variety of sampling problems. In this article, the class of linear homogeneous estimators is investigated for the area sampling frame used in agricultural surveys. It is shown that the commonly used estimators belong to this class, and results are obtained comparing these estimators with other estimators in the class. In previous work in agriculture surveys where the problem is to estimate the population total using an area sampling frame, the estimator has been formulated by assigning values to the sampling segments, so the segments are treated as the measurement units as well as the sampling units. We formulate the class of linear homogeneous estimators directly in terms of farms as the measurement unit and use this formulation, which contains the commonly used estimators, to provide a better understanding of the estimation problem. Alternatives to presently used estimators are given, practical aspects of the various estimators are discussed, and some variance inequalities are obtained.

Key Words:

• Closed segment estimator
• Horvitz-Thompson estimator
• Label dependence
• Linear homogeneous estimator
• Multiplicity estimator
• Open segment estimator
• Weighted segment estimator