标题： 回归模型中未知观测分布的位移参数估计 显示英文标题

标题： Estimation of the shift parameter in regression models with unknown distribution of the observations

摘要： 本文致力于研究在观测时间分布未知的情况下，半参数回归模型中的位移参数估计问题。 因此，我们提出了一种随机算法，该算法考虑了观测时间分布的估计。 我们证明了所提出的估计量几乎必然收敛，并且具有渐近正态性。 本文的主要结果是：在回归函数的正则性假设较少的情况下，得到的渐近方差与已知分布情况下的渐近方差相同。 从这个意义上讲，我们改进了Bercu和Fraysse的近期工作。 显示英文摘要

摘要： This paper is devoted to the estimation of the shift parameter in a semiparametric regression model when the distribution of the observation times is unknown. Hence, we propose to use a stochastic algorithm which takes into account the estimation of the distribution of the observation times. We establish the almost sure convergence of our estimator and the asymptotic normality. The main result of the paper is that, with little assumptions on the regularity of the regression function, the asymptotic variance obtained is the same as when the distribution is known. In that sense, we improve the recent work of Bercu and Fraysse.