Variance Estimation in Complex Surveys Third International Conference

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 – n n n Introduction (Chapter 1) Textbook Methods (Chapter 1) Replication-Based Methods n n n Random Group (Chapter 2) Balanced Half-Samples (Chapter 3) Jackknife (Chapter 4) Bootstrap (Chapter 5) Taylor Series (Chapter 6) Generalized Variance Functions (Chapter 7) 2

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 3

Chapter 1: Introduction 5. Probability sampling design, 8. Characteristic of interest, - 4

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, 5

Chapter 1: Introduction 14. Expectation and variance - 16. Estimator of variance - 6

Textbook Methods 1. Design: srs wor of size Estimator: Variance Estimator: 7

Textbook Methods 2. Design: srs wor at both the first and second stages of sampling Estimator: Variance Estimator: 8

Replication-Based Methods 9

Chapter 2: The Method of Random Groups n n n Interpenetrating samples Replicated samples Ultimate cluster Resampling Random groups 10

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 sampling methodology (iii) Repeat until obtained, samples are 11

Chapter 2: The Method of Random Groups Common estimation procedure: n n Editing procedures Adjustments for nonresponse Outlier procedures Estimator of parameter 12

Chapter 2: The Method of Random Groups Common measurement process: n n Field work Callbacks Clerical screening and coding Conversion to machine-readable form 13

Chapter 2: The Method of Random Groups Estimators of the Parameter of Interest, n Random group estimators n Overall estimators 14

Chapter 2: The Method of Random Groups Two Examples: Population total Ratio 15

Chapter 2: The Method of Random Groups Estimators of 16

Chapter 2: The Method of Random Groups Properties: 17

Chapter 2: The Method of Random Groups Confidence Intervals: 18

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 19

Chapter 3: Variance Estimation Based on Balanced Half-Samples average number of customers served by Montreal restaurants on a Monday night 20

Chapter 3: Variance Estimation Based on Balanced Half-Samples Textbook Estimator of Variance 21

Chapter 3: Variance Estimation Based on Balanced Half-Samples Random Group Estimator of Variance k = 2 independent random groups are available 22

Chapter 3: Variance Estimation Based on Balanced Half-Samples Half-Sample Methodology 23

Chapter 3: Variance Estimation Based on Balanced Half-Samples Choosing a Manageable Number, k, of Half. Samples 24

Chapter 3: Variance Estimation Based on Balanced Half-Samples 25

Chapter 3: Variance Estimation Based on Balanced Half-Samples Properties of the Balanced Half-Sample Methods 26

Chapter 3: Variance Estimation Based on Balanced Half-Samples Usage with Multistage Designs 27

Chapter 3: Variance Estimation Based on Balanced Half-Samples Balanced Half-Sample Methodology 28

Chapter 3: Variance Estimation Based on Balanced Half-Samples Alternative Half-Sample Estimators of Variance 29

Chapter 4: The Jackknife Method Quenouille (1949) – bias reduction Tukey (1958) – variance estimation testing interval estimation Resampling 30

Basic Methodology Chapter 4: The Method Random Jackknife sample Random groups Parameter Estimator 31

Chapter 4: The Jackknife Method Drop out m Pseudovalue Quenouille’s estimator Variance estimator Special case 32

Chapter 4: The Jackknife Method Full-sample estimator Variance estimator 33

Chapter 4: The Jackknife Method Example: ratio 34

Chapter 4: The Jackknife Method Usage in Stratified Sampling Drop out observation(s) from individual strata 35

Chapter 4: The Jackknife Method Application to Cluster Sampling Example Drop out ultimate clusters 36

Chapter 5: The Bootstrap Method 37

Chapter 5: The Bootstrap Method 38

Chapter 5: The Bootstrap Method 39

Chapter 5: The Bootstrap Method 40

Chapter 5: The Bootstrap Method 41

Chapter 5: The Bootstrap Method 42

Chapter 5: The Bootstrap Method 43

Chapter 6: Taylor Series Methods 44

Chapter 6: Taylor Series Methods n n First-order Taylor series approximation MSE 45

Chapter 6: Taylor Series Methods 46

Chapter 7: Generalized Variance Functions 1. Population total, 2. Estimator of the total, 3. Relative variance, 4. 47