Bivariate censored regression relying on a new estimator of the joint distribution function

Olivier Lopez (1) , Philippe Saint-Pierre (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

In this paper we study a class of $M-$estimators in a regression model under bivariate random censoring and provide a set of sufficient conditions that ensure asymptotic $n^{1/2}-$convergence. The cornerstone of our approach is a new estimator of the joint distribution function of the censored lifetimes. A copula approach is used to modelize the dependence structure between the bivariate censoring times. The resulting estimators present the advantage of being easily computable. A simulation study enlighten the finite sample behaviour of this technique.

Mots clés: i.i.d. representations

Mots clés: Bivariate censoring; $M-$estimation; Regression modeling; Copula functions; Kaplan-Meier estimator; i.i.d. representations.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Olivier Lopez, Philippe Saint-Pierre. Bivariate censored regression relying on a new estimator of the joint distribution function. 2011. ⟨hal-00584379⟩