Suppose the random vector $(X,Y)$ satisfies the regression model $Y=m(X)+sigma (X)arepsilon$, where $m(cdot)=E(Y|cdot),$ $sigma^{2}(cdot)=mbox{Var}(Y|cdot)$ belongs to some parametric class ${sigma _{heta}(cdot):heta in Theta}$ and $arepsilon$ 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 $sigma _{heta}(cdot)$ when $m(cdot)$ 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.
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机译：假设随机向量$（X，Y）$满足回归模型$ Y = m（X）+ sigma（X） varepsilon $，其中$ m（ cdot）= E（Y | cdot），$ $ sigma ^ {2}（ cdot）= mbox {Var}（Y | cdot）$属于某个参数类别$ { sigma _ { theta}（ cdot）： theta in Theta } $和$ varepsilon $独立于$ X $。响应$ Y $受随机权利检查，并且完全观察到协变量$ X $。当$ m（ cdot）$未知时，针对$ sigma _ { theta}（ cdot）$提出了一种新的估计程序。它基于在审查情况下扩展到条件方差的非线性最小二乘估计。建立了所提出估计量的一致性和渐近正态性。该估计器通过模拟进行研究，并且在疲劳寿命数据分析中有重要的应用。
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