Recent Developments in Nonparametric Density Estimation
非参数密度估计的近期发展AI 解读 ↓
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非参数密度估计的近期发展
- 研究问题
- 非参数密度估计有哪些方法与发展方向，传统估计、受限似然、自适应平滑及多元降维方法各自处理什么问题？
- 方法与思路
- 文章综述直方图、核与正交级数估计，讨论受限和惩罚似然、筛估计、自适应方法及投影寻踪，并介绍相关研究方向。
- 材料陈述的贡献
- 摘要称综述覆盖了以往综述和书籍遗漏的主题，并将传统密度估计、自适应平滑和多元投影寻踪纳入同一讨论范围。
- 阅读关注点
- 应核对各类方法的约束、平滑参数选择和计算代价，区分综述已有结果与作者评价，并留意文章所处年代的文献边界。
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- 来源为未注明稿件版本的OpenAlex索引摘要。这是历史性综述，“近期”对应文章当时；摘要不能提供各方法的完整条件或支持当前优劣判断。
原文摘要
Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject. The early density estimation methods, such as the histogram, kernel estimators, and orthogonal series estimators are still very popular, and recent research on them is described. Different types of restricted maximum likelihood density estimators, including order-restricted estimators, maximum penalized likelihood estimators, and sieve estimators, are discussed, where restrictions are imposed upon the class of densities or on the form of the likelihood function. Nonparametric density estimators that are data-adaptive and lead to locally smoothed estimators are also discussed; these include variable partition histograms, estimators based on statistically equivalent blocks, nearest-neighbor estimators, variable kernel estimators, and adaptive kernel estimators. For the multivariate case, extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive. A method of multivariate density estimation that did not spring from a univariate generalization is described, namely, projection pursuit density estimation, in which both dimensionality reduction and density estimation can be pursued at the same time. Finally, some areas of related research are mentioned, such as nonparametric estimation of functionals of a density, robust parametric estimation, semiparametric models, and density estimation for censored and incomplete data, directional and spherical data, and density estimation for dependent sequences of observations.