基于加权顺序统计量的加性噪声鲁棒尺度估计
Robust Scale Estimation in Additive Noise via Weighted Order Statistics
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中文总结 AI 辅助
该研究提出一种基于加权顺序统计量的非参数鲁棒框架，用于估计弱稀疏系统中加性噪声的尺度，将其应用于连续时间随机过程高频观测，成功获取分数布朗运动和稳定莱维噪声的尺度估计器。
中文摘要 AI 辅助
本手稿开发了一种非参数且鲁棒的框架，用于估计弱稀疏系统中加性噪声的尺度。该方法不要求噪声序列具有独立性、规定的依赖性或时间正则性。我们引入一类顺序统计量估计器，其基于将排序后的观测值与从参考噪声分布生成的确定性或随机代理进行比较。这种纯空间方法避免了初步滤波或时间去相关，因此保留了潜在信号的稀疏性结构。我们为加权损失函数建立了非渐近集中不等式，其界将信号的贡献与排序噪声和代理之间的差异分离开来。随后，我们在独立和相关 regime（状态）中控制该代理差异，包括重尾参考律。最后，我们将该方法应用于连续时间随机过程的高频观测，在存在低变差加性扰动的情况下，获得了分数布朗运动和稳定莱维噪声的尺度估计器。
英文摘要
This manuscript develops a non-parametric and robust framework for estimating the scale of additive noise in weakly sparse systems. The method does not require independence, prescribed dependence, or temporal regularity of the noise sequence. We introduce a class of order-statistic estimators based on comparing the sorted observations with deterministic or random proxies generated from a reference noise distribution. This purely spatial approach avoids preliminary filtering or temporal decorrelation, and therefore preserves the sparsity structure of the latent signal. We establish non-asymptotic concentration inequalities for weighted loss functions, with bounds that separate the contribution of the signal from the discrepancy between the ordered noise and the proxy. We then control this proxy discrepancy in independent and correlated regimes, including heavy-tailed reference laws. Finally, we apply the method to high-frequency observations of continuous-time stochastic processes, obtaining scale estimators for fractional Brownian motion and stable Lévy noise in the presence of lower-variation additive perturbations.
