13_complex_variance

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

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ) +...
View Full Document

## 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.

### Page1 / 26

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online