Tilted Least-Squares Parameter Estimation of Linear Regression Models in the Presence of Outliers

Biqiang Mu; Er-Wei Bai; Wei Xing Zheng

doi:10.1109/CDC49753.2023.10384312

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Conference proceeding

Tilted Least-Squares Parameter Estimation of Linear Regression Models in the Presence of Outliers

Biqiang Mu, Er-Wei Bai and Wei Xing Zheng

2023 62nd IEEE Conference on Decision and Control (CDC), pp.2464-2470

Conference on Decision and Control (CDC) (Singapore, Singapore, 12/13/2023–12/15/2023)

12/2023

DOI: 10.1109/CDC49753.2023.10384312

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Abstract

The least squares estimator is the most popular identification method. In the absence of prior knowledge on the unknown noise, uniform weights on all samples are often as-sumed. In reality, potentially unknown contamination is always present and the uniform weights are not necessarily the best. Further, explicit information about the nature of contamination is usually absent. To this end, a relaxed-tilted least squares method is proposed here to assign unequal weights so that the effect of undesired noise contamination can be mitigated. The relaxed-tilted least squares method tilts the uniform prior on the samples so as to move the uniform distribution in a direction that enjoys the smallest estimation error in the neighborhood of the uniform distribution. Theoretical results are established including the ability of outlier removal and the guaranteed parameter convergence in the presence of outliers. Numerical algorithms are proposed and simulated, which support the theoretical derivations.

Estimation error

Parameter estimation

Linear regression

Numerical simulation

Numerical models

Contamination

Least mean squares methods

Robust least squares

Outliers

Heavy-tailed noises

System identification

Details

Title: Subtitle: Tilted Least-Squares Parameter Estimation of Linear Regression Models in the Presence of Outliers
Creators: Biqiang Mu - Chinese Academy of Sciences
Er-Wei Bai - University of Iowa, Electrical and Computer Engineering
Wei Xing Zheng - Western Sydney University
Resource Type: Conference proceeding
Publication Details: 2023 62nd IEEE Conference on Decision and Control (CDC), pp.2464-2470
Conference: Conference on Decision and Control (CDC) (Singapore, Singapore, 12/13/2023–12/15/2023)
DOI: 10.1109/CDC49753.2023.10384312
Publisher: IEEE
Date published: 12/2023
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984572944102771

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