Second-order asymptotically optimal statistical classification

Blind Source Separation based on Second-Order Statistics with Asymptotically Optimal Weighting

Asymptotically minimum variance second-order estimation for complex circular processes

This paper addresses asymptotically minimum variance (AMV) of parameter estimators within the class of algorithms based on second-order statistics for estimating parameter of strict-sense stationary complex circular processes. As an application, the estimation of the frequencies of cisoids for mixed spectra time series containing a sum of cisoids and an MA process is considered. r 2005 Elsevier...

Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation

We study the differential equation ẍ(t) = a(t)V ′(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) → l > 0 as |t| → ∞. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t)→ −1 as t→ −∞ and x(t) → 1 as t → ∞. The assumptions allow l − a(t) to change sign for arbitrarily large values of |...

Second Order Hadamard Differentiability in Statistical Applications

A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limiting distributions of a class of generalized Crame r von Mises type test statistics, which include some proposed new ones for the tests of goodness of fit in the 3-sample problems, the tests in linear...

The Second Order Spectrum and Optimal Convergence

The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and eigenspaces. The convergence to eigenspaces is new, while the convergence rate for eigenvalues improves on the previous estimate by an order of magnitude.