Penalized maximum likelihood and semiparametric second-order efficiency

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the ``nonparametric component'' of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.Comment: Published at http://dx.doi.org/10.1214/009053605000000895 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A second-order stochastic dominance portfolio efficiency measure

summary:In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency using convexity property of CVaR to speed up the computation. The efficiency measure represents a distance between the tested portfolio and its least risky dominating SSD efficient portfolio. We show that this measure is consistent with the second-order stochastic dominance relation. We find out that this measure is convex and we use this result to describe the set of SSD efficient portfolios. Finally, we illustrate our results on a numerical example