1. 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

2. 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)

3. 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

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

5. 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, -

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

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

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

9. Replication-Based Methods

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

11. 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,

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

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

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

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

16. Chapter 2: The Method of Random Groups Estimators of

17. Chapter 2: The Method of Random Groups Properties:

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

19. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

34. Chapter 4: The Jackknife Method Example: ratio

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

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

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 5: The Bootstrap Method

44. Chapter 6: Taylor Series Methods

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

46. Chapter 6: Taylor Series Methods

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