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Nonparametric estimation via local estimating equations, with applications to nutrition calibration

Author

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  • Carroll, Raymond J.
  • Ruppert, David
  • Welsh, A. H.

Abstract

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a parameter depending on a predictor. The nonparametric component is estimated via local polynomials with loess or kernel weighting, asymptotic theory is derived for the latter. In keeping with the estimating equation paradigm, variances of the nonparametric function estimate are estimated using the sandwich method, in an automatic fashion, without the need typical in the literature to derive asymptotic formulae and plug-in an estimate of a density function. The same philosophy is used in estimating the bias of the nonparametric function, i.e., we use an empirical method without deriving asymptotic theory on a case-by-case basis. The methods are applied to a series of examples. The application to nutrition is called nonparametric calibration after the term used for studies in that field. Other applications include local polynomial regression for generalized linear models, robust local regression, and local transformations in a latent variable model. Extensions to partially parametric models are discussed.

Suggested Citation

  • Carroll, Raymond J. & Ruppert, David & Welsh, A. H., 1997. "Nonparametric estimation via local estimating equations, with applications to nutrition calibration," SFB 373 Discussion Papers 1997,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199717
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    References listed on IDEAS

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    1. Ruppert, D. & Wand, M.P. & Holst, U. & Hossjer, O., "undated". "Local Polynomial Variance Function Estimation," Statistics Working Paper _007, Australian Graduate School of Management.
    2. Carriquiry, Alicia L. & Fuller, Wayne A., 1996. "A Semiparametric Approach to Estimating Usual Intake Distributions," Staff General Research Papers Archive 1036, Iowa State University, Department of Economics.
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    1. Maca, J. D. & Carroll, Raymond J. & Ruppert, David, 1997. "Nonparametric kernel and regression spline estimation in the presence of measurement error," SFB 373 Discussion Papers 1997,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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