A b s t r a c t. The application of the ML method in linear regression requires a parametric form for the error density. When this is not available, the density may be parameterized by its cumulants (~i) and the ML then applied. Results , (i+2)/2 are obtained when the standardized cumulants (~/~) satisfy ~/~ = ~i+2/~2 = O(v i) as v-~ 0 for i > 0.

We study an infinite chain of transport equations for cumulants which appears in modeling the dynamics of a momentumless turbulent planar wake. The method of compatible differential constraints for formulating its integrability properties is applied. The compatibility conditions obtained make it possible to realize a reduction of the original infinite chain of transport equations and to present...

The theory of the periodic structure of nth-order statistics of cyclostationary time-series is developed. This theory is the generalization of the existing theory of the periodic structure of second-order moments of cyclostationary time-series to orders greater than two and is therefore called the theory of higher-order cyclostationarity. The theory’s central parameters are moments and cumulant...

The method of cumulants is a standard technique used to analyze dynamic light-scattering data measured for polydisperse samples. These data, from an intensity-intensity autocorrelation function of the scattered light, can be described in terms of a distribution of decay rates. The method of cumulants provides information about the cumulants and the moments of this distribution. However, the met...

In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize thirdand fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the...

We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about R-diagonal elements. Our investigations do not assume the trace property for the considered linear functionals. Introduction ...

In several cases, a sequence of free cumulants that counts certain binary plane trees corresponds to classical the decreasing versions same trees. Using two new operations on we call insertion and decomposition, prove this surprising phenomenon holds for families troupes. We give simple characterization troupes, showing they are plentiful. Troupes provide broad framework generalizing results kn...

Ghost imaging (GI) is a technique to retrieve images by correlating intensity fluctuations. In this Letter, we present novel scheme for GI referred as second-order cumulants (SCGI). The image retrieved from fluctuation information, and resolution may be enhanced compared traditional GI. We experimentally performed SCGI reconstruction, the results are in agreement with theoretical predictions.

We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable m...