Using copula information in wavelet estimation of bivariate density function based on censorship observations

Abstract

This article discusses the nonparametric estimation of a bivariate density function using copula information under right censoring. We propose an adaptive estimator based on wavelet methods and the formulae for the asymptotic mean integrated squared error(MISE) is used to get the near optimal rate on a large functional class of regular densities. In particular, the asymptotic formulae for MISE in the context of kernel density estimators is derived in the case of censoring. Finally, the consistency of the proposed estimators is established and its effectiveness is validated through a numerical simulations.

Keywords:

• Adaptive estimation
• censored data
• copula
• bi-dimensional density
• wavelets

Acknowledgements

The authors thank the referees and the associated editor for insightful comments that helped them to improve the article significantly. Esmaeil Shirazi would like to acknowledge Gonbad Kavous University for the partial support of this research through a Discovery Research Grant with number 6.165.

Disclosure statement

No potential conflict of interest was reported by the authors.