Minimax estimation with thresholding and its application to wavelet analysis
具有阈值化性质的极小极大估计及其小波分析应用AI 解读 ↓
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具有阈值化性质的极小极大估计及其小波分析应用
- 研究问题
- 能否构造只将较小系数置零、同时具有极小极大性质的估计器，从而兼顾参数估计与模型选择的需要？
- 方法与思路
- 作者构造具有阈值化性质的极小极大估计器，将推荐方法用于小波分析，并与同时面向估计和模型选择的已有方法比较。
- 材料陈述的贡献
- 摘要称，所构造的估计器实现了阈值化与极小极大性质，部分估计器渐近最优，推荐方法在所述小波比较中表现最好。
- 阅读关注点
- 应核对风险函数、参数空间及阈值规则，区分极小极大和渐近最优结论，并查看小波比较所用方法、场景与评价指标。
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- 仅据版本未注明的 OpenAlex 摘要，不能核验风险界或比较结果；所谓最好限于摘要所述比较，不能外推为所有场景下的优势。
原文摘要
Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James–Stein estimator is such an estimator, having a property called minimaxity. However, the estimator considers only one reduced model, namely the origin. Hence it reduces no coefficient estimator to zero or every coefficient estimator to zero. In many applications including wavelet analysis, what should be more desirable is to reduce to zero only the estimators smaller than a threshold, called thresholding in this paper. Is it possible to construct this kind of estimators which are minimax? In this paper, we construct such minimax estimators which perform thresholding. We apply our recommended estimator to the wavelet analysis and show that it performs the best among the well-known estimators aiming simultaneously at estimation and model selection. Some of our estimators are also shown to be asymptotically optimal.