A matrix function useful in the estimation of linear continuous-time models

In a recent publication Chen & Zadrozny (2001) derive some equations for efficiently computing eA and ∇ eA, its derivative. They employ an expression due to Bellman (1960), Snider (1964) and Wilcox (1967) for the differential deA and a method due to Van Loan (1978) to find the derivative ∇eA. The present note gives a) a short derivation of ∇ eA by way of the Bellman-Snider-Wilcox result, b) a shorter derivation without using it. In both approaches there is no need for Van Loan’s method.Peer Reviewe

Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalitzation of Lenng's domination result

The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of L¨owner partial ordering of symmetric matrices is used

On two matrix derivatives by Kollo and von Rosen

The article establishes relationships between the matrix derivatives of F with respect to X as introduced by von Rosen (1988), Kollo and von Rosen (2000) and the Magnus-Neudecker (1999) matrix derivative. The usual transformations apply and the Moore-Penrose inverse of the duplication matrix is used. Both X and F have the same dimension

On best affine unbiased covariance-preserving prediction of factor scores

This paper gives a generalization of results presented by ten Berge, Krijnen, Wansbeek & Shapiro. They examined procedures and results as proposed by Anderson & Rubin, McDonald, Green and Krijnen, Wansbeek & ten Berge. We shall consider the same matter, under weaker rank assumptions. We allow some moments, namely the variance Ω of the observable scores vector and that of the unique factors Ψ to be singular. We require T'Ψ T > 0 where T Λ T' is a Schur decomposition of Ω. As usual the variance of the common factors Φ, and the loadings matrix A will have full column rank

A note on the scalar Haffian

In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic $X^2$ test for equality of correlation matrices, and a Wald test statistic derived from Neudecker and Wesselman's (1990) expression of the asymptotic variance matrix of the sample correlation matrix.

A recursion formula for expected negative and positive powers of the central Wishart distribution

We use Haff’s fundamental identity to express the expectation of Sp in lower-order terms, where S follows the central Wishart distribution.Peer Reviewe

Some applications of the matrix Haffian in connection with differentiable matrix functions of a central Wishart variate

In this paper we revisit Haff's seminal work on the matrix Haffian as we proposed to call it. We review some results, and give new derivations. Use is made of the link between the matrix Haffian ÑF and the differential of the matrix function, dF

Matrix methods for econometric research

This thesis consists of two parts. The first part is a selfcontained survey of matrix methods relevant for econometric research. It consists of four chapters, the most important of which is the fourth. The other chapters are introductory and to a large extent standard. (There are perhaps two non-standard elements: the Kronecker matrix product which plays such a vital role in modern econometrics, and the matrix series). The fourth chapter deals with the interplay of matrices and differential calculus. Its aim is to suppress as much as is possible of the matrix elements when applying differential calculus to matrices. A series of basic theorems is being established. A varied collection of examples illustrates the methods. They are taken from current econometric literature. A comparison of the procedures used in this thesis, and the traditional procedures is not carried out, in order to safe clarity. The second part of the thesis consists of eight reprints of articles, (co-)written by the author. The majority of them are connected with matrix methods, some more than the others. Apart from matrix methods, they cover fields of research like consumption theory, business tests, input-output analysis, spatial equilibrium analysis

A recursion formula for expected negative and positive powers of the central Wishart distribution (p. 201-206)

We use Haff's fundamental identity to express the expectation of Sp in lower-order terms, where S follows the central Wishart distribution