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The obtained results are applied to hypotheses testing problems aiming at comparing the optimal values of several risk-averse convex stochastic programs on the basis of samples of the underlying random vectors. We also consider nonasymptotic tests based on confidence intervals on the optimal values of the stochastic programs obtained using the stochastic mirror descent algorithm. Numerical simulations show how to use our developments to choose among different distributions and on the considered class of risk-averse stochastic programs the asymptotic tests show better results.<\/jats:p>","DOI":"10.1137\/16m1104639","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T11:53:02Z","timestamp":1525780382000},"page":"1337-1366","source":"Crossref","is-referenced-by-count":11,"title":["A Central Limit Theorem and Hypotheses Testing for Risk-averse Stochastic Programs"],"prefix":"10.1137","volume":"28","author":[{"given":"Vincent","family":"Guigues","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Volker","family":"Kr\u00e4tschmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Shapiro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"atypb1","unstructured":"E. 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