Abstract
In this paper, we consider wavelet analysis to obtain an estimator of a copula function based on censored data. We show that optimal convergence rates for the mean integrated squared error (MISE) of linear wavelet-based function estimators are exact under right censoring model. Moreover, we derive asymptotic formulae for MISE. Finally, the simulation results and the analysis of real data validate the proposed procedure.
Highlights
Copulas and their applications in statistics have become a rather popular phenomenon
We show that our estimator obtains the optimal convergence rates under mean integrated squared error (MISE) by accepting some mild conditions
We proposed a linear wavelet estimator and provided its asymptotic formulae for mean integrated square error
Summary
Copulas and their applications in statistics have become a rather popular phenomenon. In [15] a new class of nonparametric estimators of copula function for bivariate censoring is described. The aim of this paper is to estimate the copula function via wavelets based on censoring. We can find several applications of wavelet estimators for copula functions in different contexts. We propose a linear wavelet-based estimation for copulas with right censored data in the observation T1 or T2. Many different estimators can be considered for a distribution function based on censoring. The weight considered in the present paper is In this form only T1 is assumed to be censored, and Y2 = T2, δ2 = 1 a.s., and C1 is independent from T1. Theorem 1 Assume that the function φ is m-differentiable, and let cj0 be the copula density estimator of c defined in (5). Our estimators can be regarded as an extension of those of [14] from complete data to randomly right censored data
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