Wavelet regression estimations for negatively associated sample

ABSTRACT

This paper considers wavelet estimations for a regression function based on negatively associated data. We provide upper bounds of mean integrated squared error of wavelet estimators in Besov space. It turns out that our theorem reduces to the theorem of Chesneau and Shirazi [Nonparametric wavelet regression based on biased data. Comm Statist Theory Methods. 2014;43:2642–2658], when the random sample is independent.

COMMUNICATED BY:

• Adrian Muntean

KEYWORDS:

• Wavelets
• mean integrated squared error
• nonparametric regression estimation
• negatively associated

AMS SUBJECT CLASSIFICATIONS:

• 42C40
• 62G07
• 62G20

Acknowledgments

The authors would like to thank the referees for their important suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research has been supported by the National Natural Science Foundation of China [No. 11771030], Guangxi Natural Science Foundation [Nos. 2017GXNSFAA198194, 2018GXNSFBA281076], the Guangxi Young Teachers Basic Ability Improvement Project [No. 2018KY0212].