Probability proportional to size sampling.

摘要

Scope and method of study. Approximate expressions for the two forms of the variance of the Horvitz and Thompson estimator are derived using four approximations for the joint inclusion probability as linear combinations of the marginal inclusion probabilities. Monte Carlo simulation studies are conducted to evaluate the variance approximations.;A general selection procedure was developed to be used with the Horvitz and Thompson estimator and a sample size of 2. Special cases of the general selection procedure were given. Some important results were verified for the marginal and the joint inclusion probabilities. A Monte Carlo simulation study was conducted to specify the general selection procedure.;Findings and conclusion. The first Monte Carlo simulation study showed that the four approximate expressions of the first variance form perform very well over all. Also, the second Monte Carlo simulation study showed that the first three approximate expressions of the second variance form perform very well when the population size is relatively large compared to the sample size.;The third Monte Carlo simulation study specified the general selection procedure that developed to be used with the Horvitz and Thompson estimator.