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Title of Journal: Acta Math Sinica

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Abbravation: Acta Mathematica Sinica

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Springer-Verlag

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DOI

10.1016/0009-2541(77)90045-6

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1439-7617

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Robust Depth–Weighted Wavelet for Nonparametric Re

Authors: Lu Lin
Publish Date: 2005/04/14
Volume: 21, Issue: 3, Pages: 585-592
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Abstract

In the nonparametric regression models the original regression estimators including kernel estimator Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data and the weights depend only on the distance between the design points and estimation points As a result these estimators are not robust to the perturbations in data In order to avoid this problem a new nonparametric regression model called the depth–weighted regression model is introduced and then the depth–weighted wavelet estimation is defined The new estimation is robust to the perturbations in data which attains very high breakdown value close to 1/2 On the other hand some asymptotic behaviours such as asymptotic normality are obtained Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and as a price to pay for the robustness the new method is slightly less efficient than the original method

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  2. Applications of k –covers
  3. The bipolar quantum drift-diffusion model
  4. Free completely J ( ℓ ) -simple Semigroups
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