7,902 research outputs found
Direction-Projection-Permutation for High Dimensional Hypothesis Tests
Motivated by the prevalence of high dimensional low sample size datasets in
modern statistical applications, we propose a general nonparametric framework,
Direction-Projection-Permutation (DiProPerm), for testing high dimensional
hypotheses. The method is aimed at rigorous testing of whether lower
dimensional visual differences are statistically significant. Theoretical
analysis under the non-classical asymptotic regime of dimension going to
infinity for fixed sample size reveals that certain natural variations of
DiProPerm can have very different behaviors. An empirical power study both
confirms the theoretical results and suggests DiProPerm is a powerful test in
many settings. Finally DiProPerm is applied to a high dimensional gene
expression dataset
Partial Multidimensional Inequality Orderings
The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It follows the dominance approach to making inequality comparisons, as developed for instance by Atkinson (1970), Foster and Shorrocks (1988) and Formby, Smith, and Zheng (1999) in the unidimensional context, and Atkinson and Bourguignon (1982) in the multidimensional context. By focusing on those below a multidimensional inequality “frontier”, we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual’s multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. We apply our approach to data from India and Mexico using monetary and non-monetary indicators of well-being.Inequality, multidimensional comparisons, stochastic dominance
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
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