Computational aspects of order pi ps sampling schemes
In an order sampling a finite population of size N has its units ordered by a ranking variable and then, a sample of the first n units is drawn. For order pi ps sampling, the target inclusion probabilities lambda = (lambda(k))(k=1)(N) are computed using a measure of size which is correlated with a variable of interest. The quantities lambda(k), however, are different from the true inclusion probabilities pi(k). Firstly, a new, simple method to compute pi(k) from lambda(k) is presented, and it is used to compute the inclusion probabilities of order pi ps sampling schemes (uniform, exponential and Pareto). Secondly, given two positively co-ordinated samples drawn with order pi ps sampling, the joint inclusion probability of a unit in both samples is approximated. This approximation can be used to derive the expected overlap or to construct an estimate of the covariance on these two samples. All presented methods use numerical integration. (c) 2007 Elsevier B.V. All rights reserved.
pi ps sampling numerical integration sample survey unequal probabilities fixed sample size order statistics permanent random numbers co-ordination over time