Positive extensions, Fejér–Riesz factorization and autoregressive filters in two variables

Positive Extensions , Fejér - Riesz Factorization and Autoregressive Filters in Two Variables

In this paper we treat the two-variable positive extension problem for trigonometric polynomials where the extension is required to be the reciprocal of the absolute value squared of a stable polynomial. This problem may also be interpreted as an autoregressive filter design problem for bivariate stochastic processes. We show that the existence of a solution is equivalent to solving a finite po...

CDSNS preprint 2000/355 POSITIVE EXTENSIONS AND RIESZ-FEJER FACTORIZATION FOR TWO-VARIABLE TRIGONOMETRIC POLYNOMIALS

In this paper the autoregressive filter problem for bivariate stochastic processes is reduced to a finite positive definite matrix completion problem where the completion is required to satisfy additional low rank conditions. The autoregressive filter problem may also be interpreted as a two-variable positive extension problem for trigonometric polynomials where the extension is required to be ...

Inert Module Extensions, Multiplicatively Closed Subsets Conserving Cyclic Submodules and Factorization in Modules

Introduction Suppose that  is a commutative ring with identity,  is a unitary -module and  is a multiplicatively closed subset of .  Factorization theory in commutative rings, which has a long history, still gets the attention of many researchers. Although at first, the focus of this theory was factorization properties of elements in integral domains, in the late nineties the theory was gener...

Relationship between Positive Variables and Stress

Two-stage Procedure in P-Order Autoregressive Process

In this paper, the two-stage procedure is considered for autoregressive parameters estimation in the p-order autoregressive model ( AR(p)). The point estimation and fixed-size confidence ellipsoids construction are investigated which are based on least-squares estimators. Performance criteria are shown including asymptotically risk efficient, asymptotically efficient, and asymptotically consist...