The efficient estimator and mean square error for the mean of a finite population are determined when a sample is available from a population that is assumed to be generated by a simple Markov process. The optimal sample allocation is derived and the consequences of ignoring the autocorrelation are examined. The best linear estimator and mean square error for random sampling are also determined and compared with the corresponding results for systematic sampling.
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B. J. N. Blight (1973) studied this question.
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