Title: Approximation methods for the Rice formula, with applications to small sample asymptotics
Authors: Anthony Almudevar - University of Rochester (United States) [presenting]
Abstract: The Rice formula was originally derived to model the intensity of level crossings made by a smooth stochastic process $X(t)$. In its multivariate extension, where $X(t)$ defines a smooth multidimensional random mapping, the Rice formula is equivalently the intensity function of the point process of solutions to a random system of equations. In this form, it has found application in a wide variety of problems in applied mathematics, physics and mathematical statistics. Although compact in form, evaluation of the Rice formula has proven to be technically challenging, largely because of the inclusion of a conditional expectation of the absolute determinant of a random matrix. We present a number of general higher order approximation methods targeted to this problem. These methods are demonstrated with a number of applications in nonlinear regression and generalized linear models.