An Introduction to Probability Theory and Its Applications, Volume II

TL;DR: In this paper, the authors considered inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals and provided computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or irregular.

TL;DR: A large deviation principle is derived for the degree distribution of Erdos-Renyi graphs near criticality and the rate functions governing this principle can be expressed explicitly in terms of relative entropies.

TL;DR: In this paper, the authors give a detailed picture of the asymptotic behavior of such lower deviation probabilities and adapt the well-known Cramer method for proving large deviations of sums of independent variables to their needs.

TL;DR: In this paper, a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the arguments are characterized. Necessary and sufficient conditions on the involved distortions to yield a multiivariate distribution function are given.