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

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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.

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Notes

  1. (i) A vector in \(\mathbb {R}^n\) is said to be \(k\)-sparse iff it contains at most \(k\) nonzero components where \(k<<n\). (ii) An estimate is said to be ‘sparsely noisy’ if a very minimum percentage of noise only is present in the estimate and that too occurs sparsely.

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Acknowledgments

We wish to thank the Associate Editor and two referees for their constructive comments which led to an improvement in some of our earlier results and also helped in improving the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India

    T. Palanisamy & J. Ravichandran

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  1. T. Palanisamy
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  2. J. Ravichandran
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Correspondence to J. Ravichandran.

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Palanisamy, T., Ravichandran, J. A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models. Stat Papers 56, 911–932 (2015). https://doi.org/10.1007/s00362-014-0614-6

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  • DOI: https://doi.org/10.1007/s00362-014-0614-6

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