Biometrika Advance Access originally published online on November 4, 2008
Biometrika 2008 95(4):919-931; doi:10.1093/biomet/asn048
Articles |
Small area estimation when auxiliary information is measured with error
43210 West Oster Drive, Maricopa, Arizona 85238, U.S.A. lynnybarra{at}hotmail.com
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287-1804, U.S.A. sharon.lohr{at}asu.edu
Received for publication 1 January 2007. Revision received 1 May 2008.
Small area estimation methods typically combine direct estimates from a survey with predictions from a model in order to obtain estimates of population quantities with reduced mean squared error. When the auxiliary information used in the model is measured with error, using a small area estimator such as the Fay–Herriot estimator while ignoring measurement error may be worse than simply using the direct estimator. We propose a new small area estimator that accounts for sampling variability in the auxiliary information, and derive its properties, in particular showing that it is approximately unbiased. The estimator is applied to predict quantities measured in the U.S. National Health and Nutrition Examination Survey, with auxiliary information from the U.S. National Health Interview Survey.
Key Words: Best linear unbiased prediction • Domain estimation • Fay–Herriot model • Mean squared error estimation
References
-
Buonaccorsi J. P. Prediction in the presence of measurement error: General discussion and an example predicting defoliation. Biometrics (1995) 51:1562–69.[Medline]
Carroll R. J., Eltinge J. L., Ruppert D. Robust linear regression in replicated measurement error models. Statist. Prob. Lett. (1993) 16:169–75.[CrossRef]
Carroll R. J., Ruppert D., Stefanski L. A. Measurement Error in Nonlinear Models (1995) New York: CRC Press.
Cheng C. L., Van Ness J. W. Statistical Regression with Measurement Error (1999) London: Arnold.
Citro C. F., Kalton G., eds. Using the American Community Survey: Benefits and Challenges. (2007) Washington, D. C: National Academy Press.
Datta G. S., Fay R. E., Ghosh M. Hierarchical and empirical multivariate analysis in small area estimation. In: Proc. Bureau Census Annu. Res. Conf. (1991) Washington, D. C: U.S. Census Bureau. 63–79.
Datta G. S., Lahiri P. A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statist. Sinica (2000) 10:613–27.
Datta G. S., Rao J. N. K., Smith D. D. On measuring the variability of small area estimators under a basic area level model. Biometrika (2005) 92:183–96.
Elliott M. R., Davis W. W. Obtaining cancer risk factor prevalence estimates in small areas: Combining data from two surveys. Appl. Statist. (2005) 54:595–609.
Fay R. E. Application of multivariate regression to small domain estimation. In: Small Area Statistics—Platek R., Rao J. N. K., Särndal C. E., Singh M. P., eds. (1987) New York: Wiley. 91–102.
Fay R. E., Herriot R. A. Estimates of income for small places: An application of James-Stein procedures to census data. J. Am. Statist. Assoc. (1979) 74:269–77.[CrossRef][Web of Science]
Fuller W. A. Measurement Error Models (1987) New York: Wiley.
Fuller W. A. Prediction of true values for the measurement error model. In: Statistical Analysis of, Measurement Error Models and Applications—Brown P. J., Fuller W. A., eds. (1990) Providence, RI: American Mathematical Society. 41–57. Contemporary Mathematics 112.
Fuller W. A., Harter R. M. The multivariate components of variance model for small area estimation. In: Small Area Statistics—Platek R., Rao J. N. K., Särndal C. E., Singh M. P., eds. (1987) New York: Wiley. 103–23.
Jiang J., Lahiri P., Wan S. M. A unified jackknife theory for empirical best prediction with M-estimation. Ann. Statist. (2002) 30:1782–810.[CrossRef]
Lohr S., Prasad N. G. N. Small area estimation with auxiliary survey data. Can. J. Statist. (2003) 31:383–96.[CrossRef]
National Center for Health Statistics. 2004 National Health Interview Survey (NHIS) Public Use Data Release: NHIS Survey Description. (2005) www.cdc.gov/nchs/nhis.htm.
National Center for Health Statistics. Analytic and Reporting Guidelines: The National Health and Nutrition Examination Survey (NHANES). (2006) Hyattville, MD: National Center for Health Statistics.
Petrov V. V. Sums of Independent Random Variables (1975) New York: Springer.
Pfeffermann D. Small area estimation—New developments and directions. Int. Statist. Rev. (2002) 70:125–44.[CrossRef]
Prasad N. G. N., Rao J. N. K. The estimation of the mean squared error of small-area estimators. J. Am. Statist. Assoc. (1990) 85:163–71.[CrossRef][Web of Science]
Rao J. N. K. Small Area Estimation (2003) New York: Wiley.
Rivest L. P., Vandal N. Mean squared error estimation for small areas when the small area variances are estimated. In: Proc. Int. Conf. Recent Adv. Surv. Sampl. (2003) Ottawa, ON: Laboratory for Research in Statistics and Probability and Statistics Canada. 197–206.
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||