THE THEORY OF UNIVARIATE SAMPLING ON SUCCESSIVE OCCASIONS UNDER THE GENERAL CORRELATION PATTERN1,2

The present paper is concerned with the various results developed for the theory of successive sampling. The different correlation patterns and the different sampling procedures assumed in the theory are described and further an attempt has been made to derive results for the general correlation pattern. Accordingly, an expression for the best (minimum variance linear unbiased) estimator is presented for the general correlation pattern where the sampling procedure adopted is a restricted one. When the special correlation pattern assumed in the derivation of results breaks down on a particular occasion, its effect on the estimator employed for that occasion is examined. Furthermore, an expression for the variance of the estimator, which is best under a special correlation pattern, is derived when that correlation pattern does not hold good. The expression so obtained is comparable with that furnished by Patterson (1950).