标题： 估计一个单调趋势 显示英文标题

标题： Estimating a monotone trend

摘要： 受全球变暖问题的启发，我们研究了一类时间序列，该序列由带有平稳波动的非减趋势组成。在单调性假设下，考虑了趋势的非参数估计。研究表明，在平稳误差的最弱条件下，内点处的重标度等值估计量收敛于 Chernoff 分布。由于等值估计量在端点处存在尖峰问题，提出了两种修正方法。证明了边界点处两个估计量的估计误差具有有趣的极限分布。通过模拟评估了逼近精度。我们处理方法的一个亮点是证明了弱收敛结果，其中涉及条件中心极限问题研究中的几种最新技术。这些弱收敛性可以在给定初始值的情况下被证明成立。 显示英文摘要

摘要： Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled isotonic es- timators at an interior point are shown to converge to Chernoff's distribution under minimal conditions on the stationary errors. Since the isotonic estimators suffer from the spiking problem at the end point, two modifications are proposed. The estima- tion errors for both estimators of the boundary point are shown to have interesting limiting distributions. Approximation accu- racies are assessed through simulations. One highlight of our treatment is the proof of the weak convergence results which involve several recent techniques developed in the study of con- ditional central limit questions. These weak convergences can be shown to hold conditionally given the starting values.