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Nonparametric additive model-assisted estimation for survey data

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  • Wang, Li
  • Wang, Suojin

Abstract

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.

Suggested Citation

  • Wang, Li & Wang, Suojin, 2011. "Nonparametric additive model-assisted estimation for survey data," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1126-1140, August.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:7:p:1126-1140
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    References listed on IDEAS

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    1. Li Wang, 2009. "Single-index model-assisted estimation in survey sampling," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 487-504.
    2. Opsomer, Jean D. & Breidt, F. Jay & Moisen, Gretchen G. & Kauermann, Goran, 2007. "Model-Assisted Estimation of Forest Resources With Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 400-409, June.
    3. Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 197-251, April.
    4. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    5. Martins-Filho, Carlos & yang, ke, 2007. "Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion," MPRA Paper 39295, University Library of Munich, Germany.
    6. Raymond L. Chambers & Alan H. Dorfman & Suojin Wang, 1998. "Limited information likelihood analysis of survey data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 397-411.
    7. F. J. Breidt & G. Claeskens & J. D. Opsomer, 2005. "Model-assisted estimation for complex surveys using penalised splines," Biometrika, Biometrika Trust, vol. 92(4), pages 831-846, December.
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    Cited by:

    1. Wang, Li & Wang, Suojin & Wang, Guannan, 2014. "Variable selection and estimation for longitudinal survey data," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 409-424.
    2. Xu, Bin & Lin, Boqiang, 2015. "How industrialization and urbanization process impacts on CO2 emissions in China: Evidence from nonparametric additive regression models," Energy Economics, Elsevier, vol. 48(C), pages 188-202.

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