Professor Grant Hillier

This paper presents new approaches to testing for exogeneity in non-parametric models with discrete regressors and instruments.

Recursive relations for objects of statistical interest have long been important for computation, and they remain so even with hugely improved computing power.

For a simplified structural equation/IV regression model with one right-side endogenous variable, we obtain the exact conditional distribution function for Moreira's (2003) conditional likelihood ratio (CLR) test

For a simplified structural equation/IV regression model with one right-side endogenous variable, we derive the exact conditional distribution function of Moreira's (2003) conditional likelihood ratio (CLR) test statistic.

We show in this paper that an iterative conditioning argument used by Hillier (2006) and Andrews, Moreira, and Stock (2007) to evaluate the cdf in the case <i>m</i> = 1 can be generalized to the case of arbitrary

In this paper we present new, very much more efficient, algorithms for computing both the top-order zonal and invariant polynomials.

For the problem of testing the hypothesis that all m coefficients of the RHS endogenous variables in an IV regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument.

For a simplified structural equation/IV regression model with one right-side endogenous variable, we obtain the exact conditional distribution function for Moreira's (2003) conditional likelihood ratio (CLR) test.

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal.

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices.

The existence of a uniformly consistent estimator for a particular parameter is well-known to depend on the uniform continuity of the functional that defines the parameter in terms of the model.

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices.