2016 | 17 | 1 | 9-24
Article title

Small Area Prediction under Alternative Model Specifications

Title variants
Languages of publication
Construction of small area predictors and estimation of the prediction mean squared error, given different types of auxiliary information are illustrated for a unit level model. Of interest are situations where the mean and variance of an auxiliary variable are subject to estimation error. Fixed and random specifications for the auxiliary variables are considered. The efficiency gains associated with the random specification for the auxiliary variable measured with error are demonstrated. A parametric bootstrap procedure is proposed for the mean squared error of the predictor based on a logit model. The proposed bootstrap procedure has smaller bootstrap error than a classical double bootstrap procedure with the same number of samples.
Physical description
  • National Institute of Statistical Sciences and USDA NASS, 1400 Independence Ave. SW, Room 6040 F, Washington, DC 20250
  • Iowa State University, 1214 Department of Statistics, Ames, IA 50010
  • DATTA, G. S., RAO, J. N. K., SMITH, D., (2005). On measuring the variability of small area estimators under a basic area level model, Biometrika, 92, 183−196.
  • DATTA, G. S., RAO, J. N. K., SMITH, D., (2012). Amendments and Corrections: On measuring the variability of small area estimators under a basic area level model, Biometrika, 99, 2, 509.
  • DATTA, G. S., RAO, J. N. K., TORABI, M., (2010). Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurements errors, Journal of Statistical Planning and Inference, 140, 2952−2962.
  • DAVIDSON, R., MACKINNON, J. G., (2007). Improving the reliability of bootstrap tests with the fast double bootstrap, Computational Statistics and Data Analysis, 51, 3259−3281.
  • FULLER, W. A., HARTER, R. M., (1987). The multivariate components of variance model for small area estimation, Small Area Statistics: An International Symposium, Platek, R., Rao, J. N. K., Sarndal, C.E. and Singh, M.P. (Eds.), John Wiley, New York, 103−123.
  • GHOSH, M., KIM, D., SINHA, K., MAITI, T., KATZOFF, M., PARSONS, V. L., (2009). Hierarchical and Empirical Bayes small domain estimation and proportion of persons without health insurance for minority subpopulations, Survey Methodology, 35, 53−66.
  • GHOSH, M., SINHA, K., (2007). Empirical Bayes estimation in finite population sampling under functional measurement error models, Journal of Statistical Planning and Inference, 137, 2759−2773.
  • HALL, P., MAITI, T., (2006). On parametric bootstrap methods for small area prediction, J.R. Statist. Soc. B, 68, 2, 221−238.
  • PFEFFERMANN, D., CORREA, S., (2012). Empirical bootstrap bias correction and estimation of prediction mean square error in small area estimation, Biometrika, 99, 457−472.
  • TORABI, M., DATTA, G., RAO, J. N. K., (2009). Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates, Scandinavian Journal of Statistics, 36, 355−368.
  • WANG, J., FULLER, W. A., (2003). The mean squared error of small area spedictors constructed with estimated area variances, Journal of the American Statistical Association, 98, 716−723.
  • YBARRA, L. M. R., LOHR, S. L., (2008). Small area estimation when auxiliary information is measured with error, Biometrika, 95, 919−931.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.