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Nonparametric kernel and regression spline estimation in the presence of measurement error

Author

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  • Maca, J. D.
  • Carroll, Raymond J.
  • Ruppert, David

Abstract

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel estimation, of which both can be used in the presence of measurement error. Within the kernel regression context, we derive the limit distribution of the SIMEX estimate. With the regression spline technique, two different methods of estimations are used. The first method is the SIMEX algorithm which attempts to estimate the bias, and remove it. The second method is a structural approach, where one hypothesizes a distribution for the independent variable which depends on estimable parameters. A series of examples and simulations illustrate the methods.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb373:199711
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    References listed on IDEAS

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    1. Sarah M. Nusser & Alicia L. Carriquiry & Kevin W. Dodd, 1995. "Semiparametric Transformation Approach to Estimating Usual Daily Intake Distributions, A," Center for Agricultural and Rural Development (CARD) Publications 95-sr74, Center for Agricultural and Rural Development (CARD) at Iowa State University.
    2. 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.
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    1. Carroll, Raymond J. & Freedman, Laurence & Pee, David, 1997. "Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models," SFB 373 Discussion Papers 1997,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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