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Estimation of Variances of Averages Based on Overlapping Samples in Repeated Surveys

by Benoit Quenneville of Statistics Canada, and
K.P. Srinath of Statistics Canada


Introduction: Surveys carried out by government agencies to obtain information on economic and social trends are usually repeated either monthly or quarterly. Since the surveys are expected to provide both estimates of levels and changes, they are based on overlapping samples. The amount of overlap between two periods of time is usually specified in advance, but also depends on births and deaths in the population. Quite often there is a need to produce annual averages of the monthly estimates, especially if the results of a single sample are subject to large sampling errors.

In this paper, a method of estimating the variances of annual averages and ratios of these averages is suggested. The method is based on fitting a linear model to the logarithm of the correlation coefficient between the estimates of monthly totals which are 'd' months apart, where d = 1, 2, ... 11. In section 2 a description of the problem is provided. In section 3 a model to estimate the correlation coefficients is proposed. We present in section 4 an application to the variance of ratios and to stratified samples. The usefulness of this model for estimating the variance of the annual averages of monthly totals of the Canadian Survey of Employment, Payrolls and Hours is examined in section 5. Finally, section 6 presents the conclusion of the study.

Published in: Proceedings of the Survey Research Methods Section, American Statistical Association, (1984), pp. 189-194.

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