摘要翻译：
线性最小二乘是一种非常著名的参数估计技术，即使在次优时也可以使用，因为它的计算量很低，而且不需要确切的噪声统计知识。令人惊讶的是，用有限多个样本来限定大误差的概率是开放的，尤其是在处理协方差未知的相关噪声时。本文分析了线性最小二乘估计在亚高斯鞅差噪声下的有限样本性能。为了分析这一重要问题，我们使用了测度界的集中。当应用这些界时，我们得到了估计量分布尾部的紧界。我们给出了以高概率保证给定精度所需样本数的快速指数收敛性。给出了估计误差范数的概率尾界。我们的分析方法简单，对估计误差使用简单的$l_{\infty}$type界限。通过仿真验证了边界的严密性。即使在最小二乘法是次优的情况下，也可以预测最小二乘法估计所需的样本数，并且为了计算的简单性，提出的界值使得预测最小二乘法估计所需的样本数成为可能。用这种通用噪声模型对最小二乘模型进行有限样本分析是一种新颖的方法。
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英文标题：
《Finite sample performance of linear least squares estimators under
  sub-Gaussian martingale difference noise》
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作者：
Michael Krikheli and Amir Leshem
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最新提交年份：
2017
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator under sub-Gaussian martingale difference noise. In order to analyze this important question we used concentration of measure bounds. When applying these bounds we obtained tight bounds on the tail of the estimator's distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability. We provide probability tail bounds on the estimation error's norm. Our analysis method is simple and uses simple $L_{\infty}$ type bounds on the estimation error. The tightness of the bounds is tested through simulation. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when least squares is sub-optimal and used for computational simplicity. The finite sample analysis of least squares models with this general noise model is novel.
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PDF链接：
https://arxiv.org/pdf/1710.11594