On the Feasibility of Basing Horvitz and Thompson's Estimator on a Sample by Rao, Hartley, and Cochran's Scheme

Abstract

Formulae for the first and second order inclusion probabilities for the Rao et al. (1962) (RHC) scheme of sampling are derived. They enable one to evaluate, for a sample drawn according to the RHC scheme, the Horvitz and Thompson's (1952) estimator (HTE) along with its unbiased variance estimator given by Yates and Grundy (1953). So, for a sample at hand thus drawn one may choose between the RHCE and the HTE for use on finding which one has the smaller coefficient of variation.

Keywords:

• First and second order inclusion probabilities
• Variance estimation

Mathematics Subject Classification:

• 62D05

Acknowledgments

The authors would like to thank Prof. J. N. K. Rao for some helpful discussions over email. The research of the first author was supported by the Grant No. 21(0539)/02/EMR-II of CSIR, India.