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A Simple Wavelet Approach to Nonparametric Regression from Recursive Partitioning Schemes

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  • Engel, J.

Abstract

Rates of convergence for nonparametric regression estimators based on recursive partitioning schemes are derived. The central idea is to consider the tree-structured regression estimator as a wavelet estimator based on the orthogonal system of Haar functions. A locally adaptive data-driven smoothing method is proposed and its performance is studied.

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  • Engel, J., 1994. "A Simple Wavelet Approach to Nonparametric Regression from Recursive Partitioning Schemes," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 242-254, May.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:2:p:242-254
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    Cited by:

    1. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Combining thresholding rules: a new way to improve the performance of wavelet estimators," LIDAM Discussion Papers ISBA 2011021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Autin, F. & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Ideal denoising within a family of tree-structured wavelet estimators," LIDAM Discussion Papers ISBA 2011002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Joachim Engel, 1997. "The multiresolution histogram," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 41-57, January.
    4. F. Autin & J.-M. Freyermuth & R. von Sachs, 2012. "Combining thresholding rules: a new way to improve the performance of wavelet estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 905-922, December.

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