The weight matrix in asymptotic distribution‐free methods

A method in which the weight matrix can be decomposed into matrices of smaller order is proposed, which makes inverting the matrix computationally less heavy and extends the usefulness of ADF methods to applications with a larger number of variables.

Abstract

An important problem with asymptotic distribution‐free (ADF) methods is the size of the weight matrix. Whereas under the assumption of normality of the observed variables the weight matrix can nicely be decomposed into two matrices of smaller order, under non‐normality this cannot be done straightforwardly. In this paper we propose a method in which the weight matrix can be decomposed into matrices of smaller order, which makes inverting the matrix computationally less heavy and extends the usefulness of ADF methods to applications with a larger number of variables. An additional advantage of our method is that the weight matrix is formulated in terms of model parameters. As a consequence, one should expect the weight matrix to be more stable than in cases in which the weight matrix is computed from the data itself. In addition, estimates of the parameters may be less biased, a problem which often arises in ADF methods.