Centre Fellows

Grant Hillier

University of Southampton

Professor of Econometrics

Selected Publications

A simple four-moment approximation to the distribution of a positive definite quadratic form, with applications to testing

The exact distribution of a quadratic form in n standard normal variables, Q; say, (or, equivalently, […]

Grant Hillier, Raymond O'Brien
10 January 2022 | CWP02/22
Improved tests for mediation

Testing for a mediation effect is important in many disciplines, but is made difficult – even […]

Grant Hillier, Kees Jan van Garderen, Noud van Giersbergen
10 January 2022 | CWP01/22
Nonparametric testing for exogeneity with discrete regressors and instruments

This paper presents new approaches to testing for exogeneity in non-parametric models with discrete regressors and […]

Katarzyna Bech, Grant Hillier
11 March 2015 | CWP11/15
Properties of the maximum likelihood estimator in spatial autoregressive models

The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot […]

Grant Hillier, Federico Martellosio
19 September 2013 | CWP44/13
Spatial circular matrices, with applications

The cumulants of the quadratic forms associated to the so-called spatial design matrices are often needed […]

Grant Hillier, Federico Martellosio
8 March 2010 | CWP06/10
Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors

Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can […]

Grant Hillier, Raymond Kan, Xiaolu Wang
11 June 2008 | CWP14/08

Latest version

Computationally efficient recursions for top-order invariant polynomials with applications

The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,…,kr(A1,…,Ar)in which each of the partitions of ki,i […]

Grant Hillier, Raymond Kan, Xiaolu Wang
20 February 2008 | CWP07/08

Latest version

Computationally efficient recursions for top-order invariant polynomials with applications
Grant Hillier, Raymond Kan, Xiaolu Wang
1 February 2009 | Journal Article
On the conditional likelihood ratio test for several parameters in IV regression

For the problem of testing the hypothesis that all m coefficients of the RHS endogenous variables […]

Grant Hillier
12 December 2006 | CWP26/06

Latest version

Exact properties of the conditional likelihood ratio test in an IV regression model

This paper was revised in May 2007. For a simplified structural equation/IV regression model with one […]

Grant Hillier
30 October 2006 | CWP23/06

Latest version

Ill-conditioned problems, Fisher information and weak instruments

The existence of a uniformly consistent estimator for a particular parameter is well-known to depend on […]

Giovanni Forchini, Grant Hillier
5 April 2005 | CWP04/05