Journal of Official Statistics, Vol.13, No.4, 1997. pp. 327339

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A Sampling Scheme with Partial Replacement

Unequal probability sampling with replacement is easier to handle, both theoretically and practically, than unequal probability sampling without replacement. However, sampling without replacement usually produces estimates that are more efficient. The sampling scheme due to Sa´nchez-Crespo and Gabeiras (1987), based on sampling with partial replacement, is a sort of compromise between sampling with and without replacement. It is an attempt to obtain a procedure that is more efficient than sampling with replacement while at the same time retaining some of the simplicity of sampling with replacement. In survey sampling practice the Sa´nchez-Crespo and Gabeiras scheme seems to provide a simple and potentially useful procedure that has always a smaller expected variance and greater stabilityfor the variance estimator than unequal probability sampling with replacement. We have also found strong evidence of better stability for the variance estimator than some of the best procedures developed up to now for sampling without replacement and unequal probabilities.

Unequal probability sampling;variance estimation.

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