A robust method for the identification of non-Gaussian autoregressive systems in colored Gaussian noise

This paper introduces a novel technique for parameter estimation of an autoregressive (AR) all-pole process under non-Gaussian noise environment using third order cumulants of the observed sequence. The proposed AR parameters estimation technique is based on formulating a particular structured matrix with entries of third order cumulants of the observed output sequence only. This matrix almost possesses a full rank structure. The observed sequence may be contaminated with additive Gaussian noise (white or colored), whose power spectral density is unknown. The system is driven by a zero-mean independent and identically distributed (i.i.d) non-Gaussian sequence. Simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to well-known methods even when the observed signal is heavily contaminated with Gaussian noise.

Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications

In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.