Исследованы зависимости между ковариационными матрицами, вычисляемыми в процессе многомерной рекурсии Левинсона. Показано, что учет выявленных взаимосвязей...

With the coefficient matrices of the polynomial matrices replacing the scalar coefficients in the standard Sylvester matrix, common factors exist if and only if this (generalized) Sylvester matrix is singular and the coefficient matrices commute. If the coefficient matrices do not commute, a...

The paper establishes error orders for integral limit approximations to the traces of products of Toeplitz matrices generated by integrable real symmetric functions defined on the unit circle. These approximations and the corresponding error bounds are of importance in the statistical analysis...

Consistency, asymptotic normality and e ciency of the maximum likelihood estimator for stationary Gaussian time series, were shown to hold in the short memory case by Hannan (1973) and in the long memory case by Dahlhaus (1989). In this paper, we extend these results to the entire stationarity...

This paper can be thought of as a remark of Li et al. (2010), where the authors studied the eigenvalue distribution μXN of random block Toeplitz band matrices with given block order m. In this paper, we will give explicit density functions of limN→∞μXN when the bandwidth grows slowly. In...