Articles |
A new approach to weighting and inference in sample surveys
Statistics Canada, Tunney's Pasture, R.H. Coats Building, 16th floor, Ottawa, Ontario, K1A 0T6, Canada jean-francois.beaumont{at}statcan.ca
Received for publication 1 May 2006. Revision received 1 January 2008.
The validity of design-based inference is not dependent on any model assumption. However, it is well known that estimators derived through design-based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values. We propose estimators that have the potential to improve the efficiency of any estimator derived under the design-based theory. Our main focus is limited to the improvement of the Horvitz–Thompson estimator, but we also discuss the extension to calibration estimators. The new estimators are obtained by smoothing design or calibration weights using an appropriate model. Our approach to inference requires the modelling of only one variable, the weight, and it leads to a single set of smoothed weights in multipurpose surveys. This is to be contrasted with other model-based approaches, such as the prediction approach, in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable-specific sets of weights. Our proposed approach is first justified theoretically and then evaluated through a simulation study.
Key Words: Extreme weight • Generalized design-based inference • Horvitz–Thompson estimator • Model-based inference • Multipurpose survey • Smoothed estimator • Smoothed weight
References
-
Basu D. An essay on the logical foundations of survey sampling, part 1. In: Foundations of Statistical Inference—Godambe V. P., Sprott D. A., eds. (1971) Toronto: Holt, Rinehart and Winston. 203–33.
Beaumont J.-F., Alavi A. Robust generalized regression estimation. Survey Methodol (2004) 30:195–208.
Beaumont J.-F., Rivest L.-P. Dealing with outliers in survey data. Handbook of Statistics, Vol. 29, Chapter 11, Sample Surveys: Theory, Methods and Inference—Pfeffermann D., Rao C. R., eds. (2008) Amsterdam: Elsevier BV.
Binder D. A. On the variances of asymptotically normal estimators from complex surveys. Int. Statist. Rev (1983) 51:279–92.
Chambers R. L. Robust case-weighting for multipurpose establishment surveys. J. Offic. Statist (1996) 12:3–32.
Deville J.-C., Särndal C.-E. Calibration estimators in survey sampling. J. Am. Statist. Assoc (1992) 87:376–82.[CrossRef][Web of Science]
Elliott M. R., Little R. J. A. Model-based alternatives to trimming survey weights. J. Offic. Statist (2000) 16:191–209.
Gwet J.-P., Rivest L.-P. Outlier resistant alternatives to the ratio estimator. J. Am. Statist. Assoc (1992) 87:1174–82.[CrossRef][Web of Science]
Isaki C. T., Fuller W. A. Survey design under the regression superpopulation model. J. Am. Statist. Assoc (1982) 77:89–96.[CrossRef][Web of Science]
Pfeffermann D., Krieger A. M., Rinott Y. Parametric distributions of complex survey data under informative probability sampling. Statist. Sinica (1998) 8:1087–1114.
Pfeffermann D., Sverchkov M. Parametric and semi-parametric estimation of regression models fitted to survey data. Sankhya (1999) B 61:166–86.
Potter F. A study of procedures to identify and trim extreme sampling weights. Proc. Survey Res. Meth. Sect (1990) Alexandria, VA: American Statistical Association. 225–30.
Rao J. N. K. Alternative estimators in PPS sampling for multiple characteristics. Sankhya (1966) A 28:47–60.
Rao J. N. K., Wu C. F. J. Resampling inference with complex survey data. J. Am. Statist. Assoc (1988) 83:231–41.[CrossRef][Web of Science]
Rao J. N. K., Wu C. F. J., Yue K. Some recent work on resampling methods for complex surveys. Survey Methodol (1992) 18:209–17.
Royall R. M. On finite population sampling theory under certain linear regression models. Biometrika (1970) 57:377–87.
Sverchkov M., Pfeffermann D. Prediction of finite population totals based on the sample distribution. Survey Methodol (2004) 30:79–92.
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