I am interested in econometrics and statistical theory with particular emphasis on optimal inference, statistical decision theory, exact and asymptotic distribution theory, tests for structural change, tests for misspecification, structural equations models, identification, conditional inference, saddlepoint approximations, higher order approximations, applications of differential geometry to statistics.

I have recently become interested in non-parametric identification, and obtained very promising results. They will be available here soon. The ARC has given me a grant (of AUD 150,000) for the period 2009-2011 to investigate this topic.

Don Poskitt, Chris Skeels and I were awarded a grant from the Australian Research Council (of AUD 280,000) for the period 2007-2009 to research into “Econometric estimation and inference with weak instruments and partially identified models”. The broad aim of this project is to develop more reliable methods of estimation and inference specifically designed to handle the problems associated with weak/partial identification.

Here are some of my working papers related to this line of research:

"Tests for Over-identifying Restrictions in Partially Identified Linear Structural Equations”, 2006, Monash University, Department of Econometrics and Business Statistics working paper (a newer version with the new title 'The Asymptotic distribution of tests for over-identification in partially identified linear structural equations" is available here). Mathematica 6 files that carry out the computations in this paper and more are available: graphs of the asymptotic densities under the null, graphs of the asymptotic densities under the alternative, comparison of asymptotic size and actual size, comparison of the asymptotic distributions of two variants of the over-identification test statistics. They have been set up to run on the freely downloadable Mathematica Player. A file describing common test statistics for over-identification can be downloaded here .

"Ill-conditioned problems, Fisher information and weak instruments" (with G. Hillier), 2005, cemmap working papers, CWP04/05.

These are my papers published  or accepted for publication:

1. “The asymptotic distribution of the LIML estimator in a partially identified structural equation”, 2008, accepted for publication in Econometric Theory  (a version with proofs of all statements is available here ).
2. “The Asymptotic Distribution of Nagar’s Bias-Adjusted TSLS Estimator under Partial Identification” , 2009, Economics Letters 105, pp. 49-52 (Some details of the proofs are available by clicking here).
   
3. “Some properties of tests for parameters that can be arbitrarily close to being unidentified”, 2009, Journal of Statistical Planning and Inference 139, pp. 3193-3199.
4. “Weighted average power similar tests for structural change for the Gaussian linear regression model”, 2008, Econometric Theory,  24/5,pp 1277-1290.
5. “The distribution of the sum of a normal and a t random variable with arbitrary degrees of freedom”, 2008, Metron,Vol MLXVI (2).
6. "A characterization of invariant tests for identification in linear structural equations”, 2008, Economics Letters 98/2, pp. 185-193.
7. "The Exact Distribution of the TSLS Estimator for a Non-Gaussian Just-Identified Linear Structural Equation”, 2007, Economics Letters, 95/1 pp. 117-123 (Some details of the proofs are available by clicking here).
8. “On the bimodality of the exact distribution of the TSLS estimator”, 2006, Econometric Theory 22, 932-946.
9. “Similar tests for covariance structures in multivariate linear models”, 2005, Journal of Multivariate Analysis, 93, 223-237.
10. “The distribution of a ratio of quadratic forms in noncentral normal variables", 2005, Communications in Statistics, Theory and Methods 34 (5), 1-10.
11. “Weighted average optimal similar tests for the covariance structure in the linear regression model”, 2005, Journal of Econometrics 124, 257-26.
12. “A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms”, 2005, Applicationes Mathematicae 32, 51-55.
13. “Conditional inference for possibly unidentified structural equations”, (with G. Hillier), 2003, Econometric Theory 19, 707-743.
14. “Optimal similar tests for structural change for the linear regression model”, 2002, Econometric Theory 18, 853-867.
15. “The exact cumulative distribution function of a ratio of quadratic forms in normal variables, with application to the AR(1) model”, 2002, Econometric Theory 18, 823-852.
16. “The density of the sufficient statistics for a Gaussian AR(1) model in terms of generalized functions”, 2000,  Statistics and Probability Letters 50, 2376-243.