Journal of Official Statistics, Vol.10, No.4, 1994. pp. 419435

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Optimal Winsorizing Cutoffs for a Stratified Finite Population Estimator

Within stratum expansion estimation is a popular method of estimating totals in a stratified finite population. However, if by chance several unusually large observations should fall in the sample, then the expansion estimator may grossly overestimate population totals. One technique to deal with this problem is to reduce sampled observations greater than a cutoff to a value closer to that cutoff, and then estimate the total using the new adjusted values. The resulting estimator is called the Winsorized estimator of a total. Although the Winsorized estimator is biased, it may have considerably smaller mean squared error than the expansion estimator. Necessarily, different Winsorizing cutoffs should be used for different strata. In this paper we examine the problem of estimating the optimum set of Winsorizing cutoffs for repeated surveys, where the cut-offs will be used for Winsorizing samples in future repeats of the survey. It is shown that an approximation to the optimum set of Winsorizing cutoffs may be obtained by expressing the cutoffs for all strata in terms of a single parameter L, and then searching for that value of L where a particular function equals zero. The function is a weighted sum of the tail probabilities and tail means above the Winsorizing cut-offs. It is found that by using simple estimates of these quantities, a good estimator of the optimum L value and hence of the optimum set of Winsorizing cutoffs may be constructed. In a computer simulation study the estimator is found to have considerably smaller mean squared error than the expansion estimator.

Finite population; expansion estimator; Winsorized estimator; simple random sampling.

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