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A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models

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  • T. Palanisamy
  • J. Ravichandran

Abstract

We propose a wavelet-based hybrid approach to estimate the variance function in a nonparametric heteroscedastic fixed design regression model. A data-driven estimator is constructed by applying wavelet thresholding along with the technique of sparse representation to the difference-based initial estimates. We prove the convergence of the proposed estimator. The numerical results show that the proposed estimator performs better than the existing variance estimation procedures in the mean square sense over a range of smoothness classes. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • T. Palanisamy & J. Ravichandran, 2015. "A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models," Statistical Papers, Springer, vol. 56(3), pages 911-932, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:911-932
    DOI: 10.1007/s00362-014-0614-6
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    References listed on IDEAS

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    1. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    2. Antoniadis, Anestis & Bigot, Jeremie & Sapatinas, Theofanis, 2001. "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 6(i06).
    3. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    4. Berger, James, 1976. "Minimax estimation of a multivariate normal mean under arbitrary quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 256-264, June.
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