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Variance Estimation in Complex Surveys. Third International Conference on Establishment Surveys Montreal, Quebec June 18-21, 2007 Presented by: Kirk Wolter, NORC and the University of Chicago. Outline of Lecture –. Introduction (Chapter 1) Textbook Methods (Chapter 1)
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Variance Estimation in Complex Surveys Third International Conference on Establishment Surveys Montreal, Quebec June 18-21, 2007 Presented by: Kirk Wolter, NORC and the University of Chicago
Outline of Lecture – • Introduction (Chapter 1) • Textbook Methods (Chapter 1) • Replication-Based Methods • Random Group (Chapter 2) • Balanced Half-Samples (Chapter 3) • Jackknife (Chapter 4) • Bootstrap (Chapter 5) • Taylor Series (Chapter 6) • Generalized Variance Functions (Chapter 7)
Chapter 1: Introduction Notation and Basic Definitions 1. Finite population, - Residents of Canada - Restaurants in Montreal - Farms in Quebec - Schools in Ottawa 2. Sample, - Simple random sampling, without replacement - Systematic sampling - Stratification - Clustering - Double sampling
Chapter 1: Introduction 5. Probability sampling design, - - 8. Characteristic of interest, - -
Chapter 1: Introduction 12. Parameter, - Proportion of residents who are employed - Total production of farms - Trend in price index for restaurants - Regression of sales on area for pharmacies 13. Estimator, -
Chapter 1: Introduction 14. Expectation and variance - - 16. Estimator of variance - - -
Textbook Methods 1. Design: srs wor of size Estimator: Variance Estimator:
Textbook Methods 2. Design: srs wor at both the first and second stages of sampling Estimator: Variance Estimator:
Chapter 2: The Method of Random Groups • Interpenetrating samples • Replicated samples • Ultimate cluster • Resampling • Random groups
Chapter 2: The Method of Random Groups The Case of Independent Random Groups (i) Draw a sample, No restrictions on the sampling methodology (ii) Replace the first sample Draw second sample, Use same sampling methodology (iii) Repeat until samples are obtained,
Chapter 2: The Method of Random Groups Common estimation procedure: • Editing procedures • Adjustments for nonresponse • Outlier procedures • Estimator of parameter
Chapter 2: The Method of Random Groups Common measurement process: • Field work • Callbacks • Clerical screening and coding • Conversion to machine-readable form
Chapter 2: The Method of Random Groups Estimators of the Parameter of Interest, • Random group estimators • Overall estimators
Chapter 2: The Method of Random Groups Two Examples: Population total Ratio
Chapter 2: The Method of Random Groups Estimators of
Chapter 2: The Method of Random Groups Properties:
Chapter 2: The Method of Random Groups Confidence Intervals:
Chapter 3: Variance Estimation Based on Balanced Half-Samples Description of Basic Techniques L strata Nh units per stratum N size of entire population nh = 2 units selected per stratum srs wr Example: restaurants in Montreal
Chapter 3: Variance Estimation Based on Balanced Half-Samples average number of customers served by Montreal restaurants on a Monday night
Chapter 3: Variance Estimation Based on Balanced Half-Samples Textbook Estimator of Variance
Chapter 3: Variance Estimation Based on Balanced Half-Samples Random Group Estimator of Variance k= 2 independent random groups are available
Chapter 3: Variance Estimation Based on Balanced Half-Samples Half-Sample Methodology
Chapter 3: Variance Estimation Based on Balanced Half-Samples Choosing a Manageable Number, k, of Half-Samples
Chapter 3: Variance Estimation Based on Balanced Half-Samples
Chapter 3: Variance Estimation Based on Balanced Half-Samples Properties of the Balanced Half-Sample Methods
Chapter 3: Variance Estimation Based on Balanced Half-Samples Usage with Multistage Designs
Chapter 3: Variance Estimation Based on Balanced Half-Samples Balanced Half-Sample Methodology
Chapter 3: Variance Estimation Based on Balanced Half-Samples Alternative Half-Sample Estimators of Variance
Chapter 4: The Jackknife Method Quenouille (1949) – bias reduction Tukey (1958) – variance estimation testing interval estimation Resampling
Chapter 4: The Jackknife Method Basic Methodology Random sample Random groups Parameter Estimator
Chapter 4: The Jackknife Method Drop out m Pseudovalue Quenouille’s estimator Variance estimator Special case
Chapter 4: The Jackknife Method Full-sample estimator Variance estimator
Chapter 4: The Jackknife Method Example: ratio
Chapter 4: The Jackknife Method Usage in Stratified Sampling Drop out observation(s) from individual strata
Chapter 4: The Jackknife Method Application to Cluster Sampling Example Drop out ultimate clusters
Chapter 6: Taylor Series Methods • First-order Taylor series approximation • MSE
Chapter 7: Generalized Variance Functions 1. Population total, 2. Estimator of the total, 3. Relative variance, 4.
