13_complex_variance

13_complex_variance - Complex Variance Estimation Lecture 13 STAT 651 Survey Sampling Methods Kaizar – p.1/26 Lecture 13 Complex Variance

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Unformatted text preview: Complex Variance Estimation Lecture 13 STAT 651: Survey Sampling Methods, Kaizar – p.1/26 Lecture 13: Complex Variance Estimation Reading: Lohr Chapter 9 Design Effects/Generalized Variance Functions Linearization Random Groups Resampling STAT 651: Survey Sampling Methods, Kaizar – p.2/26 1. Design Effects / GVFs Recall the design effect: deff = ˆ V “ ˆ θ under complex sampling ” ˆ V “ ˆ θ as if design had been SRS ” To use: 1. Estimate variance assuming simple random sampling 2. Multiply this variance by deff Recall the Generalized Variance Function: For Example: ˆ V ` ˆ t ´ = a ˆ t 2 + b ˆ t To use: 1. Calculate the variance using the provided function STAT 651: Survey Sampling Methods, Kaizar – p.3/26 Deff/GVF: Pros and Cons Pros Easy to use Cons Deff: must be able to calculate variance under SRS Lots and lots of approximations and assumptions Estimates of variance may themselves have large variance or bias Use caution with α-level CIs and tests. STAT 651: Survey Sampling Methods, Kaizar – p.4/26 2. Linearization Used to calculate the variance of complicated nonlinear estimators (e.g., ratios). Taylor series is a way to mathematically approximate a nonlinear function by a linear function. This is what we used to estimate the variance of a sample ratio in the SRS setting. STAT 651: Survey Sampling Methods, Kaizar – p.5/26 Taylor Series Nonlinear function: h ( x ) Taylor series: h ( x ) = h ( a ) + h ′ ( a )( x- a ) + 1 2 h ′′ ( a )( x- a ) 2 + ··· + R = h ( a ) +...
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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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13_complex_variance - Complex Variance Estimation Lecture 13 STAT 651 Survey Sampling Methods Kaizar – p.1/26 Lecture 13 Complex Variance

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