Replicate Variance Estimation and High Entropy Variance Approximation Authors: John Preston & Tamie Henderson Presenter: Greg Griffiths
Motivation • Current use of replicate variance estimation techniques for ABS Surveys • Interest in extension to pps sampling schemes
pij The pps samplers dream Estimate variances without calculating joint inclusion probabilities pij Jaroslav Hájek
High Entropy Sampling Schemes • Conditional Poisson (Hajek 1964) • Independently include unit i in sample with probability pi i=1,…,N. If total sample size ^smaller or larger than desired then reject sample and start again. • Random Systematic • Sort U randomly, select r~U(0,1), select unit u as kth sample unit if Σu-1pi <r+k-1<= Σupi • Pareto Sampling (Saavedra 1995 & Rosén 1997) • Choose ri i=1,…,N iid U(0,1) • Calculate Qi=ri(1-pi)/pi (1-ri) • Select n units with smallest values of Qi
Approximations to Var(ŶHT) for High Entropy Sampling Schemes -continued
Annual Manufacturing Survey • ~330 000 Manufacturing businesses in the population • Interested in detailed industry estimates and broad industry estimates within State • Budget supports collection of data from 5 500 businesses. Insufficient sample for detailed industry by state stratification.
pi for Manufacturing Survey Simulation Study • Stratify by broad industry and size • Calculate maximum stratum sample size needed to satisfy both broad industry by state and fine industry requirements • Iteratively adjust selection probabilities of units within state by fine industry until they aggregate to desired stratum sample sizes by state and by fine industry • For simulation study – 60 000 samples selected using Random Systematic and Pareto sampling from the Food and Beverages broad industry.