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摘要翻译：
设$(X_i)_{i=1,...,n}$是一个可能的非平稳序列，使得$\mathscr{L}(X_i)=P_n$if$i\leq n\theta$和$\mathscr{L}(X_i)=q_n$if$i>n\theta$,其中$0<\theta<1$是待估计的变化点的位置。我们在经验测度的基础上构造了一类估计量，并在通过函数族$\mathcal{F}$定义的测度空间上构造了半范数。证明了该估计量的相合性，并给出了一般条件下的收敛速度。特别地，对于包括长程相关序列甚至非平稳序列在内的许多过程，都可以达到$1/N$速率。该方法对已有的参数和非参数变点估计结果进行了统一、推广和改进，适用于独立序列、短程相关序列和长程相关序列。
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英文标题：
《Optimal rate of convergence for nonparametric change-point estimators
for nonstationary sequences》
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作者：
Samir Ben Hariz, Jonathan J. Wylie, Qiang Zhang
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that $\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if $i>n\theta$, where $0<\theta <1$ is the location of the change-point to be estimated. We construct a class of estimators based on the empirical measures and a seminorm on the space of measures defined through a family of functions $\mathcal{F}$. We prove the consistency of the estimator and give rates of convergence under very general conditions. In particular, the $1/n$ rate is achieved for a wide class of processes including long-range dependent sequences and even nonstationary ones. The approach unifies, generalizes and improves on the existing results for both parametric and nonparametric change-point estimation, applied to independent, short-range dependent and as well long-range dependent sequences.
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PDF链接：
https://arxiv.org/pdf/710.4217
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