Linear sufficiency and linear admissibility in a continuous time Gauss–Markov model

This paper considers the problem of estimation in a linear model when a stochastic process instead of a random vector is observed. Estimators obtained as integrals of the observed process are studied. Characterizations of linear sufficiency and admissibility similar to those given in the classical linear model are obtained in this context. Moreover, a definition of generalized ridge estimators in continuous time is introduced and also a characterization of such estimators is given.     

Legendre–Gauss–Lobatto spectral collocation method for nonlinear delay differential equations

A Legendre–Gauss–Lobatto spectral collocation method is introduced for the numerical solutions of a class of nonlinear delay differential equations. An efficient algorithm is designed for the single‐step scheme and applied to the multiple‐domain case. As a theoretical result, we obtain a general convergence theorem for the single‐step case. Numerical results show that the suggested algorithm enjoys high‐order accuracy both in time and in the delayed argument and can be implemented in a robust and efficient manner. Copyright © 2013 John Wiley & Sons, Ltd.     

Normal Linear Regression Models With Recursive Graphical Markov Structure

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model (≡WMANOVA model). Here these models are extended in a natural way to normal linear regression models whose LFs continue to admit such recursive factorizations, from which maximum likelihood estimators and likelihood ratio (LR) test statistics can be derived by classical linear methods. The central distribution of the LR test statistic for testing one such multivariate normal linear regression model against another is derived, and the relation of these regression models to block-recursive normal linear systems is established. It is shown how a collection of nonnested dependent normal linear regression models (≡Wseemingly unrelated regressions) can be combined into a single multivariate normal linear regression model by imposing a parsimonious set of graphical Markov (≡Wconditional independence) restrictions.     

Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction–diffusion equations

In this paper, we introduce the concept of norm-to-weak continuous process in a Banach space, and obtain the existence of pullback attractors for this kind of process. Then we give a new method for proving the existence of the pullback attractors. As an application, we obtain the existence of pullback attractors for nonautonomous reaction–diffusion equation in with exponential growth of the external force.