This paper describes a method for carrying out non-asymptotic inference on partially identifi ed parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation of a model's structural parameters....

We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and covariances of multivariate normal distributions; and we improve...

By equal mean, two skew-symmetric families with the same kernel are quite similar, and the tails are often very close together. We use this observation to approximate the tail distribution of the skew-normal by the skew-normal-Laplace, and accordingly obtain a normal function approximation to...