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摘要翻译：
近年来，小波理论的发展在信号处理、积分变换的快速算法以及图像和函数表示方法中产生了应用。最后一个应用激发了人们对小波应用于统计和实验数据分析的兴趣，在有效分析、处理和压缩噪声信号和图像方面取得了许多成功。这是一篇选择性的评论文章，试图综合一些非参数曲线估计中的非线性小波方法的最新工作及其在各种应用中的作用。在简要介绍了小波理论之后，我们详细讨论了几个小波收缩和小波阈值估计器，这些估计器散见于文献中，在或多或少的标准设置下发展起来，用于密度估计。观测数据或去噪数据模型作为一个带有加性噪声的信号的观测数据。这些方法大多适合于一般的正则化概念，并适当选择惩罚函数。本文还讨论了在统计学主要领域的应用范围，如部分线性回归模型和函数指数模型。通过仿真和实例验证了这些方法的有效性。
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英文标题：
《Wavelet methods in statistics: Some recent developments and their
applications》
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作者：
Anestis Antoniadis
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in wavelet applications to statistics and to the analysis of experimental data, with many successes in the efficient analysis, processing, and compression of noisy signals and images. This is a selective review article that attempts to synthesize some recent work on ``nonlinear'' wavelet methods in nonparametric curve estimation and their role on a variety of applications. After a short introduction to wavelet theory, we discuss in detail several wavelet shrinkage and wavelet thresholding estimators, scattered in the literature and developed, under more or less standard settings, for density estimation from i.i.d. observations or to denoise data modeled as observations of a signal with additive noise. Most of these methods are fitted into the general concept of regularization with appropriately chosen penalty functions. A narrow range of applications in major areas of statistics is also discussed such as partial linear regression models and functional index models. The usefulness of all these methods are illustrated by means of simulations and practical examples.
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PDF链接：
https://arxiv.org/pdf/712.0283
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