Schumann, Keith Daniel (2005-08). Resampling confidence regions and test procedures for second degree stochastic efficiency with respect to a function. Doctoral Dissertation. Thesis uri icon


  • 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
    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.

publication date

  • August 2005