7_ratio_estimation

7_ratio_estimation - SRS: Ratio and Regression Estimation...

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SRS: Ratio and Regression Estimation Lecture 7 STAT 651: Survey Sampling Methods, Kaizar – p.1/29
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ecture 7: Ratio and Regression Estimation Reading: Lohr Chapter 4, sections 1-3 Two types of ratios Estimate Bias Variance Uses for Ratio Estimation Regression Estimation Difference Estimation STAT 651: Survey Sampling Methods, Kaizar – p.2/29
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Types of Ratios (Estimands) 1. 1 N N s i =1 y i x i Numerator and denominator both measured on all units Divide numerator by denominator for each unit Average over the units 2. 1 N N i =1 y i 1 N N i =1 x i Numerator and denominator both measured on all units Average the numerator and denominator separately Divide the averages STAT 651: Survey Sampling Methods, Kaizar – p.3/29
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Estimand/Estimate for a Ratio Estimand: B = ¯ y U ¯ x U = t y t x Estimator: ˆ B = ¯ y ¯ x = ˆ t y ˆ t x STAT 651: Survey Sampling Methods, Kaizar – p.4/29
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Example: 2002 Pittsburgh Jewish Community Study n=982, N=10000 Goal: Estimate the number of children per adult in the Jewish community STAT 651: Survey Sampling Methods, Kaizar – p.5/29
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Bias: Approach 1 E b ˆ B B = E b ¯ y ¯ x B = STAT 651: Survey Sampling Methods, Kaizar – p.6/29
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Bias: Results 1 CV x ) r V p ˆ B P Cor p ˆ B, ¯ x P When is this small?
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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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7_ratio_estimation - SRS: Ratio and Regression Estimation...

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