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A simple nonparametric estimator of a monotone regression function

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  • Dette, Holger
  • Neumeyer, Natalie
  • Pilz, Kay F.

Abstract

In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values ˆm(i/N) (i = 1, . . . ,N) of the regression function to use these “data” for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventially used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study.

Suggested Citation

  • Dette, Holger & Neumeyer, Natalie & Pilz, Kay F., 2003. "A simple nonparametric estimator of a monotone regression function," Technical Reports 2003,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200326
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    References listed on IDEAS

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    1. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
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    Cited by:

    1. Victor Aguirregabiria, 2006. "Another Look at the Identification of Dynamic Discrete Decision Processes: With an Application to Retirement Behavior," 2006 Meeting Papers 169, Society for Economic Dynamics.
    2. Dette, Holger & Pilz, Kay F., 2004. "On the estimation of a monotone conditional variance in nonparametric regression," Technical Reports 2004,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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