Skip to main content
×
Home
    • Aa
    • Aa

NONPARAMETRIC REGRESSION IN THE PRESENCE OF MEASUREMENT ERROR

  • Susanne M. Schennach (a1)
Abstract

We introduce a nonparametric regression estimator that is consistent in the presence of measurement error in the explanatory variable when one repeated observation of the mismeasured regressor is available. The approach taken relies on a useful property of the Fourier transform, namely, its ability to convert complicated integral equations into simple algebraic equations. The proposed estimator is shown to be asymptotically normal, and its rate of convergence in probability is derived as a function of the smoothness of the densities and conditional expectations involved. The resulting rates are often comparable to kernel deconvolution estimators, which provide consistent estimation under the much stronger assumption that the density of the measurement error is known. The finite-sample properties of the estimator are investigated through Monte Carlo experiments.This work was made possible in part through financial support from the National Science Foundation via grant SES-0214068. The author is grateful to the referees and the co-editor for their helpful comments.

Copyright
Corresponding author
Address correspondence to Susanne M. Schennach, Department of Economics, University of Chicago, 1126 E. 59 St., Chicago, IL 60637; smschenn@alum.mit.edu.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Andrews, D.W.K. (1991) Asymptotic normality of series estimators for nonparametric and semiparametric regression models. Econometrica59, 307345.

Borus, M.E. & G.Nestel (1973) Response bias in reports of father's education and socioeconomic status. Journal of the American Statistical Association68, 816820.

Bowles, S. (1972) Schooling and inequality from generation to generation. Journal of Political Economy80, S219S251.

Carroll, R. & P.Hall (1988) Optimal rates of convergence for deconvolving a density. Journal of the American Statistical Association83, 11841186.

Fan, J. (1991b) On the optimal rates of convergence for nonparametric deconvolution problems. Annals of Statistics19, 12571272.

Fan, J. & Y.K.Truong (1993) Nonparametric regression with errors in variables. Annals of Statistics21, 19001925.

Freeman, R.B. (1984) Longitudinal analysis of the effects of trade unions. Journal of Labor Economics2, 126.

Hausman, J., W.Newey, & J.Powell (1995) Nonlinear errors in variables: Estimation of some Engel curves. Journal of Econometrics65, 205233.

Li, T. & Q.Vuong (1998) Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis65, 139165.

Liu, M. & R.Taylor (1989) A consistent nonparametric density estimator for the deconvolution problem. Canadian Journal of Statistics17, 427438.

Morey, E.R. & D.M.Waldman (1998) Measurement error in recreation demand models: The joint estimation of participation, site choice, and site characteristics. Journal of Environmental Economics and Management35, 262276.

Politis, D.N. & J.P.Romano (1999) Multivariate density estimation with general flat-top kernels of infinite order. Journal of Multivariate Analysis68, 125.

Schennach, S.M. (2004) Estimation of nonlinear models with measurement error. Econometrica72, 3375.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 5
Total number of PDF views: 30 *
Loading metrics...

Abstract views

Total abstract views: 108 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd May 2017. This data will be updated every 24 hours.