Browse Theses

This thesis summarizes research on methods for symbolic computation in statistics. The contribution to this area is the development of two groups of symbolic computation algorithms and procedures: one for the symbolic computation of the cumulants of either linear or non-linear functions and the other for the symbolic computation of asymptotic expansions involving either cumulants of derivatives of the log likelihood function (McCullagh, 1987) or mixed log likelihood derivatives (Barndorff-Nielsen, 1988). This type of symbolic computation, in which all of the formulae are expressed in tensor notation, is common in statistical theory and practice. Some of these expansions have been derived by hand (McCullagh, 1987; Barndorff-Nielsen, 1988). The derivation of these expansions is typically a laborious task and can involve exceedingly complicated algebra. When derived by hand they can be extremely time consuming and the potential for error is large. The purpose of this research was to develop systematic methods or algorithms for deriving and evaluating expressions common in statistical theory and practice. Based upon the algorithms, it should be straightforward to build efficient software tools for assisting statisticians to derive expressions both correctly and in a fraction of the time taken by hand and for assisting statisticians to evaluate the derived formulae in specified cases both efficiently and without writing extensive computer programs.