Summary
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 When this happens, conventional parametric and nonparametric regression techniques are no longer valid. This is further complicated when one instead wants to fit a generalized linear model to the collected data. We consider two different estimation techniques. The first method is the SIMEX (SIMulation Extrapolation) 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. For both methods, two different knot selection methods are developed.
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References
Carroll, R. J., Kxichenhoff, H., Lombard, F., Stefanski, L. A. (1996). Asymptotics for the SIMEX estimator in structural measurement error models. Journal of the American Statistical Association, 91, 242–250.
Carroll, R. J., Maca, J. D., and Ruppert, D. (1997). Nonparametric kernel and regression spline estimation in the presence of measurement error. Preprint.
Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995), Measurement Error in Nonlinear Models. London: Chapman and Hall.
Cook, J. R. & Stefanski L. A. (1994). Simulation-extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association., 89, 1314–1328.
Eilers, P. H. C. & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89–121.
Fan, J. K, Truong, Y. K. (1993). Nonparametric regression with errors in variables. Annals of Statistics, 21, 1900–1925.
Hastie, T. h Tibshirani, R. (1990). Generalized Additive Models, Chapman and Hall, New York.
Stefanski, L. A., & Cook, J. R. (1995). Simulation-Extrapolation: The measurement error jackknife. Journal of the American Statistical Association, 90, 1247–1256.
Wasserman, L. & Roeder, K. (1997). Bayesian density estimation Using mixtures of normals. Journal of the American Statistical Association, to appear.
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© 1998 Physica-Verlag Heidelberg
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Carroll, R.J., Maca, J.D., Wang, S. (1998). Nonparameteric Regression Splines for Generalized Linear Measurement Error Models. In: Galata, R., Küchenhoff, H. (eds) Econometrics in Theory and Practice. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-47027-1_3
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DOI: https://doi.org/10.1007/978-3-642-47027-1_3
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-642-47029-5
Online ISBN: 978-3-642-47027-1
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