FINITE SAMPLE DEVIATION AND VARIANCE BOUNDS FOR FIRST ORDER AUTOREGRESSIVE PROCESSES

被引：0

作者：

Gonzalez, Rodrigo A. ^{[1
]}

Rojas, Cristian R. ^{[1
]}

机构：

[1] KTH Royal Inst Technol, Div Decis & Control Syst, Stockholm, Sweden

来源：

2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING | 2020年

基金：

瑞典研究理事会;

关键词：

Autoregressive Processes; Non-Asymptotic Estimation; Least Squares; Finite Sample Analysis; EXPONENTIAL INEQUALITIES; TIME IDENTIFICATION; MARTINGALES;

D O I：

10.1109/icassp40776.2020.9053095

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by at least a positive epsilon from its true value. Our results consider both stable and unstable processes. Afterwards, we obtain problem-dependent non-asymptotic bounds on the variance of this estimator, valid for sample sizes greater than or equal to seven. Via simulations we analyze the conservatism of our bounds, and show that they reliably capture the true behavior of the quantities of interest.

引用

页码：5380 / 5384

页数：5

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