Strong Consistency of Variable Selection for Stationary Linear Stochastic Systems

被引：0

作者：

Zhao Wenxiao ^{[1
,2
]}

Yin, G. George ^{[3
]}

Bai Er-Wei ^{[4
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[4] Univ Iowa, Dept Elect & Comp Engn, Iowa City, IA 52242 USA

来源：

PROCEEDINGS OF THE 38TH CHINESE CONTROL CONFERENCE (CCC) | 2019年

基金：

美国国家科学基金会;

关键词：

Variable Selection; Linear Stochastic System; Strong Consistency; IDENTIFICATION; LASSO; ORDER;

D O I：

10.23919/chicc.2019.8866312

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider the variable selection for linear stochastic systems. A modified LASSO-type estimator is introduced. Then based on the classical persistent excitation (PE) for systems identification, the strong consistency of the estimates is established. i.e.. the zero elements in the unknown parameter vector being correctly identified and estimates for the nonzero elements in the unknown parameter vector converging to the true values with probability one. Compared with the existing results on similar topics, the strong consistency of estimates is established while in existing literature only the convergence in probability was obtained. For this, new theoretical analysis method is adopted in this paper.

引用

页码：1719 / 1723

页数：5

共 50 条

[21] OBSERVABILITY OF MULTI-DIMENSIONAL LINEAR STATIONARY SYSTEMS WITH STOCHASTIC INPUTS
KACZOREK, T
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES TECHNIQUES, 1970, 18 (04): : 327 - &
[22] RESPONSE OF LINEAR VIBRATORY SYSTEMS TO NON-STATIONARY STOCHASTIC IMPULSES
SRINIVASAN, SK
SUBRAMANIAN, R
KUMARASWAMY, S
JOURNAL OF SOUND AND VIBRATION, 1967, 6 (02) : 169 - +
[23] Some strong consistency results in stochastic regression
da Silva, Joao Lita
JOURNAL OF MULTIVARIATE ANALYSIS, 2014, 129 : 220 - 226
[24] CONSISTENCY OF BAYESIAN PROCEDURES FOR VARIABLE SELECTION
Casella, George
Giron, F. Javier
Martinez, M. Lina
Moreno, Elias
ANNALS OF STATISTICS, 2009, 37 (03): : 1207 - 1228
[25] A Procedure for Constructing Optimum Functional Filters for Linear Stationary Stochastic Systems
M. A. Kamenshchikov
I. V. Kapalin
Moscow University Computational Mathematics and Cybernetics, 2018, 42 (4) : 163 - 170
[26] Strong consistency in nonlinear stochastic regression models
Skouras, K
ANNALS OF STATISTICS, 2000, 28 (03): : 871 - 879
[27] Strong consistency of the distributed stochastic gradient algorithm
Gan, Die
Liu, Zhixin
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), 2019, : 5082 - 5087
[28] Strong consistency of the stationary bootstrap under ψ-weak dependence
Hwang, Eunju
Shin, Dong Wan
STATISTICS & PROBABILITY LETTERS, 2012, 82 (03) : 488 - 495
[29] CONTROL OF LINEAR STOCHASTIC-SYSTEMS WITH UNKNOWN VARIABLE PARAMETERS
VASILEV, VE
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1976, (04): : 108 - 123
[30] On consistency and optimality of Bayesian variable selection based on -prior in normal linear regression models
Mukhopadhyay, Minerva
Samanta, Tapas
Chakrabarti, Arijit
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2015, 67 (05) : 963 - 997

← 1 2 3 4 5 →