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Nonparametric additive model-assisted estimation for survey data. (English) Zbl 1216.62064
Summary: An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select the significant auxiliary variables. The proposed method is sufficiently fast to analyze large survey data of high dimension within seconds. The performance of the proposed method is assessed empirically via simulation studies.

62G08 Nonparametric regression and quantile regression
62D05 Sampling theory, sample surveys
62H12 Estimation in multivariate analysis
62G05 Nonparametric estimation
Full Text: DOI
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