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Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error

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  • Stephen J. Iturria
  • Raymond J. Carroll
  • David Firth

Abstract

We consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory. Diagnostics are presented for distinguishing additive and multiplicative measurement error. Data from a nutrition study are analysed by using the methods. The results from a simulation study are presented and the performances of the methods are compared.

Suggested Citation

  • Stephen J. Iturria & Raymond J. Carroll & David Firth, 1999. "Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 547-561.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:3:p:547-561
    DOI: 10.1111/1467-9868.00192
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    Cited by:

    1. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno & Gasco, Loreta, 2002. "Measurement Error Models with Nonconstant Covariance Matrices," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 395-415, August.
    2. Elena Biewen & Sandra Nolte & Martin Rosemann, 2008. "Multiplicative Measurement Error and the Simulation Extrapolation Method," IAW Discussion Papers 39, Institut für Angewandte Wirtschaftsforschung (IAW).
    3. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    4. Danh Nguyen & Damla şentürk & Raymond Carroll, 2008. "Covariate-adjusted linear mixed effects model with an application to longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 459-481.

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