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.