EMPIRICAL COMPARISON OF VARIOUS APPROXIMATE ESTIMATORS OF THE VARIANCE OF HORVITZ THOMPSON ESTIMATOR UNDER SPLIT METHOD OF SAMPLING
Keywords:
Variance Estimation, Relative Bias, Relative Mean Square Error, Efficiency, Split Method of Sample Selection.Abstract
Under inclusion probability proportional to size (IPPS) sampling, the exact second- order inclusion probabilities are often very difficult to obtain, and hence variance of the Horvitz- Thompson estimator and Sen-Yates-Grundy estimate of the variance of Horvitz-Thompson estimator are difficult to compute. Hence the researchers developed some alternative variance estimators based on approximations of the second-order inclusion probabilities in terms of the first order inclusion probabilities. We have numerically compared the performance of the various alternative approximate variance estimators using the split method of sample selection
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References
Asok, C. and Sukhatme, B.V. (1976). On Sampford’s procedure of unequal
probability sampling without replacement, J. Amer. Stat. Assoc., 71, p. 912-
Brewer, K.R.W. (2002). Combined Survey Sampling Inference, Weighing
Basu’s Elephants, Arnold Publisher.
Brewer, K.R.W. and Donadio, M.E. (2003). The high entropy variance of the
Horvitz-Thompson estimator, Survey Methodology, 29, p. 189-196.
Cochran, W.G. (1982). Sampling Techniques, 3rd Ed., John Wiley & Sons.
Deville, J.C. and Tille, Y. (1998). Unequal probability sampling without
replacement through a splitting method, Biometrika, 85(1), p. 89-101.
Gabler, S. (1984). On unequal probability sampling: Sufficient conditions for
the superiority of sampling without replacement, Biometrika, 71, p. 171-175.
Hajek, J. (1964). Asymptotic theory of rejective sampling with varying
probabilities from a finite population, Annals of Mathematical Statistics, 35, p.
-1523.
Hartley, H.O. and Rao, J.N.K. (1962). Sampling with unequal probabilities
and without replacement, The Annals of Mathematical Statistics, 33, p. 350-
Haziza, D., Mecatti, F., and Rao, J.N.K. (2008). Evaluation of some
approximate variance estimators under the Rao-Sampford unequal probability
sampling design, Int. J. Statist. Vol. LXVI, No.1, 91-108.
Henderson, T. (2006). Estimating the variance of Horvitz-Thompson
estimator, Bachelor’s Thesis, Australian National University.
Hidiroglou, M.A. and Gray, G. B. (1980). Construction of joint probability of
selection of for systematic pps sampling, Applied Statistics, 29, p. 107-112.
Horvitz, D.G. and Thompson, D.J. (1952). A generalization of sampling
without replacement from finite universe, J. Amer. Statist. Assoc., 47, p. 663-
Matei, A and Tille, Y. (2005). Evaluation of variance approximations
estimators in maximum entropy sampling with unequal probability and fixed
sample size, Journal of Official Statistics, 21, No.4, p. 543-570.
Mukhopadhyay, P. (1998). Theory and Methods of Survey Sampling.
Prentice-Hall of India, New Delhi.
Rosen, B. (1991). Variance estimation for systematic pps-sampling, Report
:15, Statistics Sweden.
Sen, A.R. (1953). On the estimation of variance in sampling with varying
probabilities, J. Ind. Soc. Agri. Statist., 5, p. 119-127.
Sukhatme, P.V. and Sukhatme, B.V. (1970). Sampling Theory of Surveys with
Applications, Asia Publishing House, Calcutta.
Yates, F. and Grundy, P.M. (1953). Selection without replacement from within
strata with probability proportional to size, J. Roy. Statist. Soc., B15, p.253-
