Asymptotic likelihood inference

grantor: University of TorontoIn this thesis, we develop a simple general formula for approximating the 'p'-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterization. Implementation is discussed in terms of computer algebra packages. A second order asymptotic method is proposed based on a sample space derivative approximation, which is used by Barndorff-Nielsen (1995), Skovgaard (1996) and Raser and Reid (1996). Comparison with other second order methods discussed by Barndorff-Nielsen and Chamberlin (1991) and DiCiccio and Martin (1993) is given. The aim here is to implement the second order inference to a standard computing software system for practical use. Numerical examples using this package are given, including inference for nonlinear regression models and generalized linear models. We also consider the recent higher order methods in the estimating function context using quasi-likelihood function. We focus on inference for a scalar parameter of interest: profile likelihood for the scalar parameter is defined and we describe a method for using this to approximate significance probabilities. Finally, some applications of the third order likelihood inference to the Gamma shape and noncentral chi-squared distribution are addressed.Ph.D