| The first chapter of this thesis is concerned with the problem of optimal decision making in the presence of parameter uncertainty. My contribution in this chapter is a unified resampling procedure for selecting an approximate risk minimizing decision rule from a parameterized class of decision rules. In addition to delivering a reduction in risk, this procedure offers the added benefit of being simple to implement while allowing one to avoid imposing restrictive parametric assumptions. The remaining two chapters in this thesis are concerned with testing for any pre-specified order of stochastic dominance between a given pair of distribution functions. I first examine the problem of testing for nth order dominance, and offer a new integral-type test for use in this context. The integral-type test possesses several attractive features, which include consistency and admissibility, along with being computationally inexpensive. Subsequently, I consider the limiting case of infinite-degree stochastic dominance (ISD). After motivating the need to develop a formal statistical test for ISD, I provide one such test and illustrate its use in an application to ranking the performance of various financial market indices. |
