 # Variance Estimation in Complex Surveys Third International Conference on Establishment Surveys Montreal, Quebec June 18-21, 2007 Presented by: Kirk Wolter,

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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

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 N h units per stratum N size of entire population n h = 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 Quenouilles 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.

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