Uniform almost sure convergence rate of wavelet estimator for regression model with mixed noise

ABSTRACT

This article considers a non parametric estimation problem in a regression model with mixed noise. A wavelet estimator is proposed by using projection of wavelet coefficients estimators. Uniform almost sure convergence rate of this wavelet estimator is derived under some mild conditions. It should be pointed out that the convergence rate of the wavelet estimator coincides with the optimal strong uniform convergence rate of non parametric estimations. Finally, simulation studies illustrate the good performances of the wavelet estimator.

KEYWORDS:

• Non parametric estimation
• strong convergence rate
• mixed noise
• wavelet

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 62G07
• 62G20
• 42C40

Acknowledgements

All authors thank the two referees for their insightful comments that helped us improve the article significantly.

Additional information

Funding

This article is supported by the National Natural Science Foundation of China (No. 12001133), Guangxi Natural Science Foundation (No. 2022JJA110008), Center for Applied Mathematics of Guangxi (GUET), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.