3-P Sampling and Some Alternatives, II

In this paper some sample selection alternatives to 3-P (probability proportional to prediction) sampling are given for the situation where no frame is available prior to sampling. The alternatives are systematic and random p.p.s. (probability proportional to size) sampling from the cumulated sizes, and random equal probability sampling. These sample selection methods make it possible to use standard estimators which are then compared with the adjusted and unadjusted 3-P estimators on three large data sets which are treated as populations. The estimators are compared on the basis of bias, error variance, and variance of the estimated variances. For these populations, the unequal probability sampling procedures are superior to equal probability sampling in terms of variances of the estimators. The systematic sampling from the cumulated Xi appears better than the 3-P procedure but both appear better than the random (with replacement) p.p.s. procedure. The large sampling fractions make the difference between with and without replacement sampling more striking, however, than it generally would be in actual practice. Forest Sci. 17:103-118.