Discussion: The Dantzig selector: statistical estimation when pp is much larger than nn

Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]Comment: Published in at http://dx.doi.org/10.1214/009053607000000451 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

From Animal Baits to Investors’ Preference: Estimating and Demixing of the Weight Function in Semiparametric Models for Biased Samples

We consider two semiparametric models for the weight function in a biased sample model. The object of our interest parametrizes the weight function, and it is either Euclidean or non Euclidean. One of the models discussed in this paper is motivated by the estimation the mixing distribution of individual utility functions in the DAX market.Mixture distribution, Inverse problem, Risk aversion, Exponential mixture, Empirical pricing kernel, DAX, Market utility function.

No need for an oracle: the nonparametric maximum likelihood decision in the compound decision problem is minimax

We discuss the asymptotics of the nonparametric maximum likelihood estimator (NPMLE) in the normal mixture model. We then prove the convergence rate of the NPMLE decision in the empirical Bayes problem with normal observations. We point to (and use) the connection between the NPMLE decision and Stein unbiased risk estimator (SURE). Next, we prove that the same solution is optimal in the compound decision problem where the unobserved parameters are not assumed to be random. Similar results are usually claimed using an oracle-based argument. However, we contend that the standard oracle argument is not valid. It was only partially proved that it can be fixed, and the existing proofs of these partial results are tedious. Our approach, on the other hand, is straightforward and short