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摘要翻译：
Hardy、Littlewood和P\'Olya提出了单调后rarrrangement算法作为函数的排序工具。假设$x$是一个单调函数，并且给出了$x$的估计值$x_n$，考虑$x_n$的单调重排$\hat{x}_n$。这个新的估计量是一致相合的。在适当的假设下，得到了$\hat{x}_n$的点态极限分布结果。该框架是通用的，允许弱相关和长程相关的平稳数据。详细介绍了它在单调密度估计和回归函数估计中的应用。
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英文标题：
《Limit properties of the monotone rearrangement for density and
regression function estimation》
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作者：
Dragi Anevski, Anne-Laure Foug\`eres (MODAL'X)
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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：
The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and P\'olya as a sorting device for functions. Assuming that $x$ is a monotone function and that an estimate $x_n$ of $x$ is given, consider the monotone rearrangement $\hat{x}_n$ of $x_n$. This new estimator is shown to be uniformly consistent. Under suitable assumptions, pointwise limit distribution results for $\hat{x}_n$ are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.
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PDF链接：
https://arxiv.org/pdf/710.4617
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