Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications

This chapter deals with multivariate right-censored survival data, and a bivariate framework. The non-parametric estimator proposed by Lopez and Saint-Pierre allows us to obtain a proper joint distribution. Moreover, it presents some desirable properties: classical empirical estimator is obtained in absence of censoring, estimates of marginal distribution lead to Kaplan-Meier estimates and it is equivariant under reversal of coordinates. Estimation of several dependence measures as Kendall's coefficient is discussed. A bootstrap procedure for multivariate survival data is derived. The chapter also discusses a regression model where the response and the covariate are both randomly right-censored. The chapter introduces the bivariate distribution estimator to estimate the quantities. It provides an asymptotic independent and indentically distributed (i.i.d.) representation for the estimators. A section focuses on the estimation of dependence measures, a bootstrap procedure and regression modeling. Finally, the chapter illustrates the applications of these methods.