An Asymptotic Variance Formula for Sampling Without Replacement with Unequal Probabilities

Document Type : Original Article

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Abstract

Asymptotic formulae for the variance of the Horvitz and Thompson Estimator for sampling with unequal probabilities without replacement have e inter previously been derived for a number of particular sampling procedures. To order N¹ these asymptotic formulae are identical. In this paper the asymptotic formula to order N is established, under a linear stochastic model, for the general class of sampling procedures in which the number of sample units is fixed and sampling is strictly without replacement.

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