Selection Procedures Using Special Estimators

Abstract

In Chapter 3 a comparison was made of those selection procedures for which the Horvitz-Thompson estimator possessed the ratio estimator property. It was mentioned, however, in Section 1.7 that certain special estimators had also been devised for use with particular selection procedures, and that in the context of these procedures they also possessed the ratio estimator property. In this Chapter the performance of these special estimators will be compared in the context of their appropriate selection procedures; that is,

• (i) Das’s estimator with Procedure 4,

• (ii) Raj’s and Murthy’s estimators with Procedure 4,

• (iii) the Rao-Hartley-Cochran (RHC) estimator with Procedure 25,

• (iv) unbiased and ratio estimators for Poisson sampling with Procedure 27,

• (v) unbiased and ratio estimators for Modified Poisson Sampling with Procedure 38,

• (vi) unbiased and ratio estimators for Collocated Sampling with Procedure 39, and

• (vii) Lahiri’s estimator with Procedures 45–46.