Density estimation via periodic scaled Korobov kernel method with exponential decay condition

研究问题: 摘要称，如何在无界域 $\mathbb{R}^d$ 上对非周期密度进行非参数估计，并给出均方积分误差（MISE）收敛界。摘要称，如何在无界域 $\mathbb{R}^d$ 上对非周期密度进行非参数估计，并给出均方积分误差（MISE）收敛界。
方法与思路: 作者提出周期缩放 Korobov 核（PSKK）方法：先用模运算把目标密度包裹为周期版本，再在缩放 Korobov 空间做核岭回归，从而推广 Kazashi 与 Nobile（2023）的核方法。
材料陈述的贡献: 摘要称，该方法去掉了原方法对密度本身周期性的要求，可估计无界域上的密度；在光滑性阶为 $\alpha$ 且具指数衰减的假设下，证明 MISE 收敛率为 $\mathcal{O}(M^{-1/(1+1/(2\alpha)+\varepsilon)})$ ，与既有核方法同阶，代价是更强的可微性与指数衰减假设。摘要称，该方法去掉了原方法对密度本身周期性的要求，可估计无界域上的密度；在光滑性阶为 $\alpha$ 且具指数衰减的假设下，证明 MISE 收敛率为 $\mathcal{O}(M^{-1/(1+1/(2\alpha)+\varepsilon)})$，与既有核方法同阶，代价是更强的可微性与指数衰减假设。
阅读关注点: 应核对：模运算包裹与缩放 Korobov 空间的具体构造、核岭回归的调参与 $M$ 的含义、指数衰减与光滑性假设的精确形式、MISE 界的证明条件，以及数值实验的设定与对比基准。应核对：模运算包裹与缩放 Korobov 空间的具体构造、核岭回归的调参与 $M$ 的含义、指数衰减与光滑性假设的精确形式、MISE 界的证明条件，以及数值实验的设定与对比基准。
阅读边界: 仅凭摘要无法判断证明细节、假设是否可放松、数值实验的可复现性与实际样本表现；摘要未说明具体数据集、带宽选择与计算复杂度。该文为 arXiv 预印本，未经同行评审验证。

DeepSeek Flash · 2026-10-15

原文摘要

We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$ . By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile (SIAM J. Numer. Anal., 2023) and eliminate its requirement for inherent periodicity of the density function. This key modification enables effective estimation of densities defined on unbounded domains. We establish rigorous mean integrated squared error (MISE) bounds, proving that for densities with smoothness of order $α$ and exponential decay, our PSKK method achieves an $\mathcal{O}(M^{-1/(1+1/(2α)+ε)})$ MISE convergence rate with an arbitrarily small $ε>0$ . While matching the convergence rate of the previous kernel approach, our method applies to non-periodic distributions at the cost of stronger differentiability and exponential decay assumptions. Numerical experiments confirm the theoretical results and demonstrate a significant improvement over traditional kernel density estimation in large-sample regimes.We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile (SIAM J. Numer. Anal., 2023) and eliminate its requirement for inherent periodicity of the density function. This key modification enables effective estimation of densities defined on unbounded domains. We establish rigorous mean integrated squared error (MISE) bounds, proving that for densities with smoothness of order $α$ and exponential decay, our PSKK method achieves an $\mathcal{O}(M^{-1/(1+1/(2α)+ε)})$ MISE convergence rate with an arbitrarily small $ε>0$. While matching the convergence rate of the previous kernel approach, our method applies to non-periodic distributions at the cost of stronger differentiability and exponential decay assumptions. Numerical experiments confirm the theoretical results and demonstrate a significant improvement over traditional kernel density estimation in large-sample regimes.

摘要来源：arXiv

笔记与分组

分类依据与纠错

Density estimation via periodic scaled Korobov kernel method with exponential decay condition

作者的期刊发表依据

代码、数据与补充材料

基于周期缩放 Korobov 核与指数衰减条件的密度估计

原文摘要

同方向的基础文献

同方向的基础文献