Parametric conditional variance estimation in location-scale models with censored data

Suppose the random vector (X,Y) satisfies the regression model Y=m(X)+sigma(X)*varepsilon,
where m(.)=E(Y|.), sigma²(.)=Var(Y|.) belongs to some parametric class {sigma _theta(.): theta in Theta} and varepsilon is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. A new estimation procedure is proposed for sigma_theta(.) when m(.) is unknown. It is based
on nonlinear least squares estimation extended to conditional variance in the censored case. The consistency and asymptotic normality of the proposed estimator are established. The estimator is studied via simulations
and an important application is devoted to fatigue life data analysis.