Order statistics approach to estimation of the dimension of the noise subspace

Model order selection and in particular determination of the dimension of the noise subspace, is an important problem in statistical signal processing. The discrete nature of the problem puts it in between detection and estimation. Standard tools from detection theory force a solution subject to arbitrary false alarm probability. On the other hand the direct maximum likelihood (ML) approach requires a penalty connection. In this paper we suggest the use of order statistics (OS) approach for the estimation of the dimension of the noise subspace. We show that the likelihood function of the ordered data has a unique non-trivial maximum with respect to the assumed dimension, and therefore we suggest an OS ML estimator. It is based on processing a single ordered sample and is, therefore, very simple. It assumes nothing about the distribution of the signal plus noise and therefore it is robust to the signal model. The suggested approach is demonstrated for i.i.d. exponential noise.