Model order estimation via penalizing adaptively the likelihood (PAL)

Abstract

This paper introduces a novel rule for model order estimation based on penalizing adatively the likelihood (PAL). The penalty term of PAL, which is data adaptive (as the name suggests), has several unique features: it is “small” (e.g. comparable to AIC penalty) for model orders, let us say n, less than or equal to the true order, denoted by n0, and it is “large” (e.g. of the same order as BIC penalty) for n>n0; furthermore this is true not only as the data sample length increases (which is the case most often considered in the literature) but also as the signal-to-noise ratio (SNR) increases (the harder case for AIC, BIC and the like); and this “oracle-like” behavior of PAL's penalty is achieved without any knowledge about n0. The paper presents a number of simulation examples to show that PAL has an excellent performance also in non-asymptotic regimes and compare this performance with that of AIC and BIC.