Variance estimation with Chao's sampling scheme

Berger, Y.G. (2005) Variance estimation with Chao's sampling scheme. Journal of Statistical Planning and Inference, 127 (1-2). pp. 253-277. ISSN 0378-3758 doi: 10.1016/j.jspi.2003.08.014

Abstract/Summary

We show that the Hájek (Ann. Math Statist. (1964) 1491) variance estimator can be used to estimate the variance of the Horvitz–Thompson estimator when the Chao sampling scheme (Chao, Biometrika 69 (1982) 653) is implemented. This estimator is simple and can be implemented with any statistical packages. We consider a numerical and an analytic method to show that this estimator can be used. A series of simulations supports our findings.