A computer algebra for sample survey theory - ARCHIVED

A system of procedures that can be used to automate complicated algebraic calculations frequently encountered in sample survey theory is introduced. It is shown that three basic techniques in sampling theory depend on the repeated application of rules that give rise to partitions: the computation of expected values under any unistage sampling design, the determination of unbiased or consistent estimators under these designs and the calculation of Taylor series expansions. The methodology is illustrated here through applications to moment calculations of the sample mean, the ratio estimator and the regression estimator under the special case of simply random sampling without replacement. The innovation presented here is that calculations can now be performed instantaneously on a computer without error and without reliance on existing formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae presently exist. The computer code developed to implement this methodology is available via anonymous ftp at fisher.stats.uwo.ca.