Bernstein-type Inequalities and Nonparametric Estimation under Near-Epoch Dependence
近历依赖下的 Bernstein 型不等式与非参数估计AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要核心是通用随机场不等式与非参数估计，时间序列仅作为特例出现，尚不足以确定所列经济学细分中的主要方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
近历依赖下的 Bernstein 型不等式与非参数估计
- 研究问题
- 不规则间距的近历依赖随机场如何获得集中不等式，索引集的有效维度又如何影响核估计的一致收敛速度和最优性？
- 方法与思路
- 作者对几何及代数近历依赖随机场推导 Bernstein 型与经验过程偏差不等式，再分析回归、密度和密度水平集等核估计。
- 材料陈述的贡献
- 摘要称，不等式的紧致程度由有效维度决定，并据此建立多类估计量的一致速度，部分方法达到最优或差一个对数因子的速度。
- 阅读关注点
- 应核对有效维度的定义、近历依赖及混合条件、空间采样布局，以及各估计问题最优速度的比较基准和适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未获验证；摘要未列具体速度和完整条件，首次发现及更新既有研究的说法尚待核验。
原文摘要
The major contributions of this paper lie in two aspects. Firstly, we focus on deriving Bernstein-type inequalities for both geometric and algebraic irregularly-spaced NED random fields, which contain time series as special case. Furthermore, by introducing the idea of "effective dimension" to the index set of random field, our results reflect that the sharpness of inequalities are only associated with this "effective dimension". Up to the best of our knowledge, our paper may be the first one reflecting this phenomenon. Hence, the first contribution of this paper can be more or less regarded as an update of the pioneering work from \citeA{xu2018sieve}. Additionally, as a corollary of our first contribution, a Bernstein-type inequality for geometric irregularly-spaced $α$-mixing random fields is also obtained. The second aspect of our contributions is that, based on the inequalities mentioned above, we show the $L_{\infty}$ convergence rate of the many interesting kernel-based nonparametric estimators. To do this, two deviation inequalities for the supreme of empirical process are derived under NED and $α$-mixing conditions respectively. Then, for irregularly-spaced NED random fields, we prove the attainability of optimal rate for local linear estimator of nonparametric regression, which refreshes another pioneering work on this topic, \citeA{jenish2012nonparametric}. Subsequently, we analyze the uniform convergence rate of uni-modal regression under the same NED conditions as well. Furthermore, by following the guide of \citeA{rigollet2009optimal}, we also prove that the kernel-based plug-in density level set estimator could be optimal up to a logarithm factor. Meanwhile, when the data is collected from $α$-mixing random fields, we also derive the uniform convergence rate of a simple local polynomial density estimator \cite{cattaneo2020simple}.