Bandwidth selectors for multivariate kernel density estimation

Kernel density estimation is an important data smooting technique. It has been applied most successfully for univariate data whilst for multivariate date its development and implementation have been relatively limited. The performance of kernel density estimators depends crucially on the bandwidth selection. Bandwidth selection in the univariate case involves selecting a scalar parameter which controls the amount of smoothing. In the multivariate case, the bandwidth matrix controls both the degree and direction of smoothing so its selection is more difficult. So far most of the research effort has been expended on automatic, data-driven selectors for univariate data. There is, on the other hand, a relative paucity of multivariate counterparts. Most of these multivariate bandwidth selectors are focused on the restricted case of diagonal matrices. In this thesis practical algorithms are constructed, with supporting theoretical justifications, for unconstrained bandwidth matrices.