In successive sampling on two occasions, the theory developed so far aims at providing the optimum estimate by combining (i) a double-sampling regression estimate from the matched portion of the sample and (ii) a simple mean based on a random sample from the unmatched portion of the sample on the second occasion. Theory has been generalized in the present note by using a double-sampling multivariate ratio estimate using $p$ auxiliary variates $(p \geqq 1)$ from the matched portion of the sample. Expressions for optimum matching fraction and of the combined estimate and its error have been derived and results are presented for some special cases which have practical applications.
"Successive Sampling With $p (p \geqq 1)$ Auxiliary Variables." Ann. Math. Statist. 43 (6) 2031 - 2034, December, 1972. https://doi.org/10.1214/aoms/1177690878