Journal of Official Statistics, Vol.14, No.2, 1998. pp. 149–162

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Sequential Poisson Sampling

Poisson sampling is a simple way to draw a probability proportional to size (pps) sample from a finite population. It also offers an easy way to update a sample while retaining as many units as possible from the previous sample, and/or to minimize overlap of different samples. A drawback of Poisson sampling is the random sample size. We present a fixed size alteration of Poisson sampling, sequential Poisson sampling, designed for, and used in, the Swedish Consumer Price Index (CPI). We show that the respective estimators associated with ordinary and sequential Poisson sampling, are both asymptotically normally distributed and unbiased as well as equally efficient. Simulations on CPI data verify approximate unbiasedness and approximate equality of variances, plus equally good performance of associated estimators of variance. Therefore, sequential Poisson sampling is preferable, because of the fixed size.

Probability proportional to size; sample coordination; sample updating; overlap control; asymptotic normality; consumer price index.

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