Residual Ratio Thresholding for Model Order 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.