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

5. 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. 6 Chapter 1: Introduction 14.Expectation and variance - 16.Estimator of variance -

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

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

9. 9 Replication-Based Methods

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

11. 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. 12 Chapter 2: The Method of Random Groups Common estimation procedure: Editing procedures Adjustments for nonresponse Outlier procedures Estimator of parameter

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

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

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

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

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

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

19. 19 Chapter 3: Variance Estimation Based on Balanced Half-Samples Description of Basic Techniques L strata N h units per stratum N size of entire population n h = 2 units selected per stratum srs wr Example: restaurants in Montreal

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

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

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

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

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

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

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

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

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

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

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

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

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

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

34. 34 Chapter 4: The Jackknife Method Example: ratio

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

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

37. 37 Chapter 5: The Bootstrap Method

38. 38 Chapter 5: The Bootstrap Method

39. 39 Chapter 5: The Bootstrap Method

40. 40 Chapter 5: The Bootstrap Method

41. 41 Chapter 5: The Bootstrap Method

42. 42 Chapter 5: The Bootstrap Method

43. 43 Chapter 5: The Bootstrap Method

44. 44 Chapter 6: Taylor Series Methods

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

46. 46 Chapter 6: Taylor Series Methods

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