# Resampling confidence regions and test procedures for second degree stochastic efficiency with respect to a function

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## Abstract

It is often desirable to compare risky investments in the context of economic decision theory. Expected utility analyses are means by which stochastic alternatives can be ranked by re-weighting the probability mass using a decision-making agent??????s utility function. By maximizing expected utility, an agent seeks to balance expected returns with the inherent risk in each investment alternative. This can be accomplished by ranking prospects based on the certainty equivalent associated with each alternative. In instances where only a small sample of observed data is available to estimate the underlying distributions of the risky options, reliable inferences are difficult to make. In this process of comparing alternatives, when estimating explicit probability forms or nonparametric densities, the variance of the estimate, in this case the certainty equivalent, is often ignored. Resampling methods allow for estimating dispersion for a statistic when no parametric assumptions are made about the underlying distribution. An objective of this dissertation is to utilize these methods to estimate confidence regions for the sample certainty equivalents of the alternatives over a subset of the parameter space of the utility function. A second goal of this research is to formalize a testing procedure when dealing with preference ranking with respect to utility. This is largely based on Meyer??????s work (1977b) developing stochastic dominance with respect to a function and more specific testing procedures outlined by Eubank et. al. (1993). Within this objective, the asymptotic distribution of the test statistic associated with the hypothesis of preference of one risky outcome over another given a sub-set of the utility function parameter space is explored.