Wavelet estimation of norms for a probability density with negatively dependent biased data

Abstract

This article considers wavelet estimations for density functions in Besov spaces based on negatively dependent biased random samples. More precisely, wavelet estimators are defined and their $L^p(1\le p<\infty )$ convergence rates are provided when the parameter μ is known and unknown, respectively.

KEYWORDS:

• Wavelet estimator
• probability density
• biased function
• negatively dependent
• Besov space

2010 MSC:

• 62G07
• 62G20
• 42C40

Acknowledgments

The authors would like to thank two referees for their important suggestions and comments, which improve the manuscript very much.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No.12101014), and the Natural Science Basic Research plan in Shaanxi Province of China (No.2020JQ-892).