The Annals of Statistics

Local polynomial regresssion estimators in survey sampling

F. Jay Breidt and Jean D. Opsomer

Full-text: Open access

Abstract

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are considerably weaker. The estimators are shown to be asymptotically design-unbiased and consistent under mild assumptions. A variance approximation based on Taylor linearization is suggested and shown to be consistent for the design mean squared error of the estimators. The estimators are robust in the sense of asymptotically attaining the Godambe–Joshi lower bound to the anticipated variance. Simulation experiments indicate that the estimators are more efficient than regression estimators when the model regression function is incorrectly specified, while being approximately as efficient when the parametric specification is correct.

Article information

Source
Ann. Statist., Volume 28, Number 4 (2000), 1026-1053.

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015956706

Digital Object Identifier
doi:10.1214/aos/1015956706

Mathematical Reviews number (MathSciNet)
MR1810918

Zentralblatt MATH identifier
1105.62302

Subjects
Primary: 62D05: Sampling theory, sample surveys
Secondary: 62G08: Nonparametric regression

Keywords
Calibration generalized regression estimation Godambe-Joshi lower bound model-assisted estimation nonparametric regression

Citation

Breidt, F. Jay; Opsomer, Jean D. Local polynomial regresssion estimators in survey sampling. Ann. Statist. 28 (2000), no. 4, 1026--1053. doi:10.1214/aos/1015956706. https://projecteuclid.org/euclid.aos/1015956706


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