doi: 10.17706/ijapm.2017.7.3.200-208
The Consistency of Wavelet Density Estimator with Heteroscedastic Measurement Error
Xiaochen Zeng
,
- College of Applied Sciences, Beijing University of Technology, Pingle Yuan 100, Beijing, 100124, P. R. China
Abstract
The wavelet deconvolution estimation based on independent and identically distributed data has made a great progress in nonparametric statistics. However, heteroscedastic measurement errors occur in many natural processes. In this current paper, we construct a practical wavelet deconvolution estimator under severely ill-posed noise and show its mean consistency over <em>Lp</em> risk (1≤<em>p</em><∞).
Keywords
- Consistency
- density estimation
- severely Ill-posed noise
- wavelet
How to Cite
Xiaochen Zeng and Jinru Wang, "The Consistency of Wavelet Density Estimator with Heteroscedastic Measurement Error," International Journal of Applied Physics and Mathematics, vol. 7, no. 3, pp. 200-208, 2017. https://doi.org/ 10.17706/ijapm.2017.7.3.200-208
Copyright & License
Copyright © 2017 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).