8_more_ratio_estimation

# 8_more_ratio_estimation - H domains(categories 2 Estimate...

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More Ratio and Regression Estimation Lecture 8 STAT 651: Survey Sampling Methods, Kaizar – p.1/8

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Lecture 8: More Ratio Estimation Reading: Lohr Chapter 4, sections 4-5 Poststratification Stratified Ratio Estimation STAT 651: Survey Sampling Methods, Kaizar – p.2/8
Recall Stratification Recall Stratified Random Sampling: ¯ y str = H s h =1 N h N ¯ y h ˆ t str = H s h =1 ˆ t h = H s h =1 N h ¯ y h STAT 651: Survey Sampling Methods, Kaizar – p.3/8

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Poststratification Ratio Estimation is the process of adjusting estimates for known population means. Poststratification is the process of adjusting estimates for known population category sizes, or known domain sizes. STAT 651: Survey Sampling Methods, Kaizar – p.4/8
Poststratified Mean 1. Group the sample into H domains (categories) 2. Estimate the mean within each domain: ¯ y h , h = 1 , . . . , H 3. Take a weighted average of the domain means ¯ y post = H s h =1 N h N ¯ y h STAT 651: Survey Sampling Methods, Kaizar – p.5/8

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Poststratified Total 1. Group the sample into

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Unformatted text preview: H domains (categories) 2. Estimate the mean within each domain: ¯ y h , h = 1 , . . . , H 3. Take a weighted sum of the domain means ˆ t ypost = H s h =1 N h ¯ y h STAT 651: Survey Sampling Methods, Kaizar – p.6/8 Variance Estimation Recall Domain Variance (assuming the sample size in the domain is large enough): V [¯ y h ] ≈ p 1-n N P s 2 yd n d We approximate the variance for the poststratified estimator using an independence approximation: V [¯ y str ] = V b H s h =1 N h N ¯ y h B = STAT 651: Survey Sampling Methods, Kaizar – p.7/8 Ratio Estimation in Stratification Two approaches: 1. Combined Ratio Estimator: ˆ t yrc = ˆ Bt x , where ˆ B = ˆ t ystr ˆ t xstr 2. Separate Ratio Estimator: ˆ t yrs = H s h =1 ˆ B h t xh , where ˆ B h = ˆ t yh ˆ t xh STAT 651: Survey Sampling Methods, Kaizar – p.8/8...
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## This note was uploaded on 07/26/2011 for the course STA 651 taught by Professor Kaizar during the Winter '11 term at Ohio State.

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8_more_ratio_estimation - H domains(categories 2 Estimate...

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