This tutorial serves as an introduction to recently developed non-asymptotic
methods in the theory of -- mainly linear -- system identification. We
emphasize tools we deem particularly useful for a range of problems in this
domain, such as the covering technique, the Hanson-Wright Inequality and the
method of self-normalized martingales. We then employ these tools to give
streamlined proofs of the performance of various least-squares based estimators
for identifying the parameters in autoregressive models. We conclude by
sketching out how the ideas presented herein can be extended to certain
nonlinear identification problems.

该论文介绍了最近在系统辨识理论中发展起来的非渐近方法，重点介绍了在该领域的一系列问题中特别有用的工具，如覆盖技术、Hanson-Wright 不等式和自标准化马丁格尔方法，并使用这些工具对用于识别自回归模型中的参数的各种最小二乘估计器的性能给出了简化的证明。最后概述了如何将所提出的思想扩展到某些非线性辨识问题。

系统辨识的非渐近理论教程

A Tutorial on the Non-Asymptotic Theory of System Identification

We study an adaptive estimation procedure called the Goldenshluger-Lepski
method in the context of reproducing kernel Hilbert space (RKHS) regression.
Adaptive estimation provides a way of selecting tuning parameters for
statistical estimators using only the available data. This allows us to perform
estimation without making strong assumptions about the estimand. In contrast to
procedures such as training and validation, the Goldenshluger-Lepski method
uses all of the data to produce non-adaptive estimators for a range of values
of the tuning parameters. An adaptive estimator is selected by performing
pairwise comparisons between these non-adaptive estimators. Applying the
Goldenshluger-Lepski method is non-trivial as it requires a simultaneous
high-probability bound on all of the pairwise comparisons. In the RKHS
regression context, we choose our non-adaptive estimators to be clipped
least-squares estimators constrained to lie in a ball in an RKHS. Applying the
Goldenshluger-Lepski method in this context is made more complicated by the
fact that we cannot use the $L^2$ norm for performing the pairwise comparisons
as it is unknown. We use the method to address two regression problems. In the
first problem the RKHS is fixed, while in the second problem we adapt over a
collection of RKHSs.

研究一种自适应估计过程，在再生核希尔伯特空间（RKHS）回归的背景下称为 Goldenshluger-Lepski 方法，该方法使用所有数据产生非自适应的估算器，通过进行成对比较选择自适应估算器。