Discussion: Topics in Estimation and Modeling for National and 

International Surveys 

Michael P. Cohen 

Senior Consultant to NORC 

1801 Pennsylvania Avenue NW 

Washington DC 20006-3608 

MPCohen@Juno.com 

Introduction

In essence, this was a session about estimation in surveys. Before discussing the individual papers, I will first make 

some brief remarks about estimation in general. I will then comment on small area estimation, the topic of two of 

the three papers. Turning to the individual papers, I first discuss the paper on small area estimation for Navarra, 

then the one on small area estimation for the Current Population Survey. Next comes the paper on weighting for the 

American Community Survey followed by a brief conclusion. 

Estimation

I want to take this opportunity to comment on estimation as a specialty within survey statistics. Often estimates are 

just weighted averages so what’s the big deal? 

In fact, there are many challenging areas for the estimation specialist: 

(1) Price indexes 

(2) Seasonal adjustment of estimates 

(3) Composite estimation and small area estimation more generally 

(4) Principal person weighting and other subtle weighting issues 

Estimation is a topic of international scope. As this session amply demonstrates, it behooves practitioners and 

researchers in estimation to pay attention to what is happening throughout the world. 

Small Area Estimation (SAE)

SAE is an important topic in estimation and its importance is increasing. The underlying principle of SAE is to 

“borrow strength” from a domain for which there is more data. This borrowing strength can introduce some bias in 

the estimates but the substantial variance reduction makes the technique very worthwhile. 

One can borrow strength from a larger geographic area or from a longer time period (see diagram). The two SAE 

papers in this session borrow strength geographically. 

In designing a survey to make estimates for small areas, one must consider whether the primary purpose is to make 

estimates of level or of change. All too often, surveys are designed as if level were of paramount importance 

whereas the analytical reports derived from the survey focus on change. 

Despite the intense activity in SAE, there is much room for further research in developing estimates, 

variance estimates, and confidence intervals that are efficient yet relatively insensitive to modeling 

assumptions. 
DirectEstimatorBorrowStrength

AcrossGeography

BorrowStrengthBorrowStrength

AcrossTimeAcrossGeography

andTime

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ways to Borrow Strength 

in Small Area Estimation

Navarra SAE

Let us now turn to the very interesting paper by Maria Ugarte, Ana Militino, and Tomas Goicoa, all with the Public 

University of Navarra. Navarra is a subnational area in Spain. I am not aware of any work of this caliber by any 

state in the United States. 

A composite estimation method is employed that “shrinks” the estimate toward a synthetic estimate and away from 

the direct one. The amount of shrinkage is controlled by a parameter called α . The largest value of α considered 

turned out to be the best. I wondered why the authors did not investigate still larger α values. Also worth 

considering are composite estimation methods that base the amount of shrinkage on variance estimates. Such 

methods offer the potential of great gains in efficiency but can be sensitive to outliers or skewness in the data. 

I was impressed by the careful and thorough testing of the estimation methods on simulated data. With regard to 

variance estimation, the authors state: “All the [variance estimation] methods proposed here tend to overestimate 

the MSE...” For most official statistical purposes, some overestimation of MSE is usually very acceptable. If the 

MSE estimate is to be used as a component of some other estimate (as in, e.g., components of variance models), 

overestimation may be as serious as underestimation. 

Current Population Survey SAE

The paper by Swamy Paravastu (U.S. Bureau of Labor Statistics), Tamara Zimmerman (U.S. Bureau of Labor 

Statistics), and Jatinder Mehta (Temple University) on SAE for the U.S. Current Population Survey is especially 

noteworthy for the clever way that it addresses nonsampling error. It employs a simple time series model to get at 

the error structure. 

A caution: components of variance techniques may lead to delicate estimation problems. This caution 

notwithstanding, this research is a real tour de force and opens up an extremely promising path. Empirical testing 

should be the next step 
 

 

 

 

 

 

 

 

American Community Survey Weighting

Turning from SAE, the last paper by Mark Asiala of the U.S. Census Bureau addresses weighting for the U.S 

American Community Survey. The challenge is to develop weights that are consistent at the both the household and 

person levels. This is a fascinating estimation problem. The method Asiala develops seems very reasonable. 

Weighting of the U.S Consumer Expenditure Surveys was a major topic of the early 1980s. Zieschang (1986, 1990) 

and Alexander and Roebuck (1986) are recommended reading. 

I would like to encourage more subject matter based analysis. As just one brief example, one would expect 

weighting up of young adults to increase estimates of the number of housing units. 

Conclusion

This session well illustrates the richness of the challenges in survey estimation and the exciting work being done in 

the area both nationally and internationally. 

Acknowledgements: I sincerely thank the authors/presenters not only for their excellent presentations but also for 

their well prepared papers given to me in advance. Tamara Rib ably chaired the session and kept everything 

running smoothly. Very special thanks to Kevin Cecco for organizing the session and inviting me to discuss. 

References 

Kimberly D. Zieschang, Sample Weighting Methods and Estimation of Totals in the Consumer Expenditure Survey, 

Journal of the American Statistical Association, Vol. 85, No. 412. (Dec., 1990), pp. 986-1001 

Kimberly D. Zieschang, A Generalized Least Squares Weighting System for the Consumer Expenditure Survey, 

American Statistical Association Proceedings of the Section on Survey Research Methods, 1986, 64-71 

Chip Alexander and Michael Roebuck, Comparison of Alternative Methods for Household Estimation, American 

Statistical Association Proceedings of the Section on Survey Research Methods, 1986, 54-63