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On the estimation of a monotone conditional variance in nonparametric regression

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  • Dette, Holger
  • Pilz, Kay F.

Abstract

A monotone estimate of the conditional variance function in a heteroscedastic, nonpara- metric regression model is proposed. The method is based on the application of a kernel density estimate to an unconstrained estimate of the variance function and yields an esti- mate of the inverse variance function. The final monotone estimate of the variance function is obtained by an inversion of this function. The method is applicable to a broad class of nonparametric estimates of the conditional variance and particularly attractive to users of conventional kernel methods, because it does not require constrained optimization techniques. The approach is also illustrated by means of a simulation study

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb475:200442
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    References listed on IDEAS

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    1. Ruppert, D. & Wand, M.P. & Holst, U. & Hossjer, O., "undated". "Local Polynomial Variance Function Estimation," Statistics Working Paper _007, Australian Graduate School of Management.
    2. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    3. 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.
    4. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    5. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
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    1. Neumeyer, Natalie, 2005. "A note on uniform consistency of monotone function estimators," Technical Reports 2005,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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