Some problems of inference in two-dimensional distributions

Abstract

This thesis is concerned with problems of, and associated with, inference in some particular two-dimensional distributions. This includes obtaining properties of parameter estimators in multiparametrie and multidimensional distributions which is generally a very messy procedure. Since the theory of how to obtain maximum likelihood estimators and their asymptotic properties is well developed, and because these asymptotic properties are deemed desirable for inferential procedures, maximum likelihood estimators should be examined, if only to enable comparisons to be made with estimators that are easier to calculate. Although the theory of maximum likelihood estimation is fairly well developed, the practical difficulties this can entail tend to be glossed over. Obtaining properties of other estimators can be even more difficult. Often only asymptotic moments, if that, can be obtained and no distributional properties. Here a variety of methods are used to extract as much information as possible about the parameter estimators. Problems associated with inference are not confined to obtaining properties of parameter estimators. It may be necessary to verify that a particular estimation scheme, such as maximum likelihood, can be used for a particular problem. In addition if such an estimation scheme is inappropriate or unwieldy, some other approach may have to be considered. As an exploratory step it may be desirable to establish distributional or probabilistic properties of the distribution involved, and some work of this kind is done in this thesis.