Replicate Variance Estimation and High Entropy Variance Approximation

  • Slides: 17
Download presentation
Replicate Variance Estimation and High Entropy Variance Approximation Authors: John Preston & Tamie Henderson

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

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

Notation

Notation

Variance and Variance Estimation

Variance and Variance Estimation

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

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

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

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

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

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

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

Rao-Wu Bootstrap

Rao-Wu Bootstrap

Rao-Wu Bootstrap - extensions

Rao-Wu Bootstrap - extensions

Replicate Version of BR 1

Replicate Version of BR 1

Replicate Version of Hajek

Replicate Version of Hajek

Annual Manufacturing Survey • ~330 000 Manufacturing businesses in the population • Interested in

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 •

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.

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

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