标题： 带有相关误差和预测变量的随机回归中的波纹估计 显示英文标题

标题： Kink estimation in stochastic regression with dependent errors and predictors

摘要： 在本文中，我们研究了回归函数\mu 在两个具有不同长程依赖（LRD）结构的随机设计模型中一阶导数（称为拐点）的跳跃点的估计问题。 该方法基于零交叉技术，并使用了高阶核。 估计量的收敛速度取决于依赖程度和回归函数\mu 的平滑性。 在一个模型中，收敛速度与固定设计情况下独立同分布误差的拐点估计的最小最大率相同，这表明该方法在最小最大意义上是最优的。 显示英文摘要

摘要： In this article we study the estimation of the location of jump points in the first derivative (referred to as kinks) of a regression function \mu in two random design models with different long-range dependent (LRD) structures. The method is based on the zero-crossing technique and makes use of high-order kernels. The rate of convergence of the estimator is contingent on the level of dependence and the smoothness of the regression function \mu. In one of the models, the convergence rate is the same as the minimax rate for kink estimation in the fixed design scenario with i.i.d. errors which suggests that the method is optimal in the minimax sense.