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Title: On solutions to estimating equations and the empirical saddlepoint approximation of their distribution Authors:  Benjamin Holcblat - University of Luxembourg (Luxembourg)
Fallaw Sowell - Carnegie Mellon University (United States) [presenting]
Abstract: Many statistics correspond to a solution to estimating equations, so that the latter are often used to conduct inference. We study solutions to estimating equations, and the empirical saddlepoint (ESP) approximation of their distribution. When estimating equations are nonlinear, they may have multiple solutions. Under general assumptions, we prove that, for any solution, there exists an arbitrary close measurable solution, and that the distribution of the solutions corresponds to the intensity measure of a point random field. If the set of solutions has no accumulation point, we establish the global consistency and asymptotic normality of the ESP approximation. Monte-Carlo simulations and an empirical application illustrate the performance of the ESP approximation.