对称空间上密度估计的下界

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-03-31 DOI:10.1016/j.spl.2025.110416

Dena Marie Asta

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引用次数: 0

摘要

我们证明了在非紧型对称空间上的核密度估计，其l2 -风险在先前的工作（Asta, 2021）中有界，实际上实现了极小极大收敛速度。有了这个结果，就完成了所有对称空间上核密度估计的故事。对欧几里德空间的证明进行改编的思想是将欧几里德空间上的向量空间运算适当地抽象为对称群的作用和Helgason-Fourier变换的再参数化，并利用非紧型对称空间的指数映射定义了一个微分同构的事实。

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Lower bounds for density estimation on symmetric spaces

We prove that kernel density estimation on symmetric spaces of non-compact type, whose

L_{2}

-risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.