Residual Ratio Thresholding for Model Order Selection

TL;DR

This paper introduces a new residual ratio thresholding method for model order selection in linear regression, offering competitive performance especially with small sample sizes, and provides a rigorous analysis of its behavior at high SNR and large samples.

Contribution

The paper presents a novel residual ratio thresholding technique for model order selection, distinct from traditional information theoretic criteria, with theoretical analysis and competitive empirical results.

Findings

RRT performs well with small sample sizes.

Theoretical analysis of RRT at high SNR and large samples.

RRT is competitive with AIC, BIC, PAL in model selection.

Abstract

Model order selection (MOS) in linear regression models is a widely studied problem in signal processing. Techniques based on information theoretic criteria (ITC) are algorithms of choice in MOS problems. This article proposes a novel technique called residual ratio thresholding for MOS in linear regression models which is fundamentally different from the ITC based MOS criteria widely discussed in literature. This article also provides a rigorous mathematical analysis of the high signal to noise ratio (SNR) and large sample size behaviour of RRT. RRT is numerically shown to deliver a highly competitive performance when compared to popular model order selection criteria like Akaike information criterion (AIC), Bayesian information criterion (BIC), penalised adaptive likelihood (PAL) etc. especially when the sample size is small.