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Replicate Variance Estimation and High Entropy Variance Approximation

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 p ps sampling schemes. Notation.

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Replicate Variance Estimation and High Entropy Variance Approximation

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  1. Replicate Variance Estimation and High Entropy Variance Approximation Authors: John Preston & Tamie Henderson Presenter: Greg Griffiths

  2. Motivation • Current use of replicate variance estimation techniques for ABS Surveys • Interest in extension to pps sampling schemes

  3. Notation

  4. Variance and Variance Estimation

  5. pij The pps samplers dream Estimate variances without calculating joint inclusion probabilities pij Jaroslav Hájek

  6. 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

  7. Approximations to Var(ŶHT) for High Entropy Sampling Schemes

  8. Approximations to Var(ŶHT) for High Entropy Sampling Schemes -continued

  9. Estimators of Approximations to Var(ŶHT) for High Entropy Schemes

  10. Rao-Wu Bootstrap

  11. Rao-Wu Bootstrap - extensions

  12. Replicate Version of BR1

  13. Replicate Version of Hajek

  14. 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.

  15. 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.

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