Volume 7 Number 3 (Jul. 2017)
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IJAPM 2017 Vol.7(3): 200-208 ISSN: 2010-362X
doi: 10.17706/ijapm.2017.7.3.200-208

The Consistency of Wavelet Density Estimator with Heteroscedastic Measurement Error

Xiaochen Zeng, Jinru Wang

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 Lp risk (1≤p<∞).

Index Terms—Consistency, density estimation, severely Ill-posed noise, wavelet.

The authors are with College of Applied Sciences, Beijing University of Technology, Pingle Yuan 100, Beijing, 100124, P. R. China (email: zengxiaochen@emails.bjut.edu.cn).

Cite: Xiaochen Zeng, 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.

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing: INSPEC(IET), CNKI, Google Scholar, EBSCO, Chemical Abstracts Services (CAS), etc.
E-mail: ijapm@iap.org
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