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Juan Antonio Cuesta Albertos, U. Cantabria Print
Thursday, 11 May 2017, 12:15 - 13:15

Juan Antonio Cuesta Albertos, Universidad de Cantabria 

Paper 1 : Models for the Assessment of Treatment Improvement: the Ideal and the Feasible

Abstract: Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new treatment significantly better than the old?'. However, this is only partially answered by some of the usual statistical tools for this task. More importantly, often practitioners are not aware of the real meaning behind these statistical procedures. We analyze these troubles from the point of view of the order between distributions, the stochastic order, showing evidence of the limitations of the usual approaches, paying special attention to the classical comparison of means under the normal model. We discuss the unfeasibility of statistically proving stochastic dominance, but show that it is possible, instead, to gather statistical evidence to conclude that slightly relaxed versions of stochastic dominance hold. 

Paper 2 : A Contamination Model for Approximate Stochastic Order

Abstract: Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic orderings are often a too strong assumption which is not supported by the data even in cases in which the researcher tends to believe that a certain variable is somehow smaller than other. Instead of considering this rigid model of stochastic order we propose to look at a more flexible version in which two distributions are said to satisfy an approximate stochastic order relation if they are slightly contaminated versions of distributions which do satisfy the stochastic ordering. The minimal level of contamination that makes this approximate model hold can be used as a measure of the deviation of the original distributions from the exact stochastic order model. Our approach is based on the use of trimmings of probability measures. We discuss the connection between them and the approximate stochastic order model and provide theoretical support for its use in data analysis, including asymptotic distributional theory as well as non-asymptotic bounds for the error probabilities of our tests. We also provide simulation results and a case study for illustration. 

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