Replicate Variance Estimation and High Entropy Variance Approximation
- Slides: 17
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
Notation
Variance and Variance Estimation
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-1 pi <r+k-1<= Σu pi • 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
Approximations to Var(ŶHT) for High Entropy Sampling Schemes -continued
Estimators of Approximations to Var(ŶHT) for High Entropy Schemes
Rao-Wu Bootstrap
Rao-Wu Bootstrap - extensions
Replicate Version of BR 1
Replicate Version of Hajek
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.
RANSYS %RB %RS PARETO %EC %RB %RS %EC Haj -3. 55 80. 4 85. 0 0. 05 82. 4 85. 5 Haj-Ber -3. 17 81. 0 85. 1 0. 50 82. 9 85. 5 Haj-Dev -3. 23 80. 6 85. 0 0. 54 82. 6 85. 6 Haj-MT -3. 23 80. 6 85. 0 0. 54 82. 6 85. 5 Haj-Boot -3. 80 81. 5 84. 7 -0. 08 83. 3 85. 3 BR 1 -0. 44 81. 3 85. 6 3. 44 83. 5 86. 2 BR 2 -0. 67 81. 1 85. 6 3. 20 83. 3 86. 1 BR 3 -0. 22 81. 5 85. 6 3. 67 83. 7 86. 2 BR 4 -0. 22 81. 5 85. 6 3. 67 83. 7 86. 2 BR-Dev -0. 12 -1. 94 81. 5 82. 1 85. 7 85. 1 3. 78 1. 87 83. 8 84. 1 86. 2 85. 7 BR-MT BR 1 -Boot
RANSYS BR 1 PARETO BR 1 -BOOT %RB %RS Haj %RB Haj-BOOT %RB %RS Meat & Meat Product 0. 19 99. 9 -0. 10 100. 6 -1. 14 98. 8 -1. 18 99. 7 Dairy Product -0. 10 153. 9 -0. 21 154. 4 -0. 66 153. 1 -0. 69 153. 4 Fruit & Vegetable Processing -0. 83 165. 0 -0. 97 165. 5 -0. 23 165. 2 -0. 12 166. 1 Oil & Fat -0. 11 155. 2 0. 14 156. 2 -0. 02 154. 8 0. 32 156. 2 Flour Mill & Cereal Food -0. 86 108. 5 -0. 93 109. 3 -0. 61 108. 6 -0. 66 109. 1 Bakery Product 0. 12 120. 0 -0. 15 120. 5 -0. 29 119. 5 -0. 37 120. 3 Other Food 0. 10 98. 5 -0. 37 99. 5 -0. 32 99. 8 -0. 28 100. 8 Beverage & Malt -0. 13 242. 2 -0. 32 242. 3 -0. 92 238. 9 -0. 91 239. 0
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