A Functional Version of the Birkhoff Ergodic Theorem for a Normal Integrand: A Variational Approach

Abstract

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points. In this case, we speak of discrete parameter models. Even though the problem is quite old and has interesting connections with testing and model selection, asymptotic theory for these models has hardly ever been studied. Therefore, we discuss consistency, asymptotic distribution theory, information inequalities and their relations with efficiency and superefficiency for a general class of $m$-estimators.

Raffaello Seri

Professor of Econometrics

My research interests include statistics, numerical analysis, operations research, psychology, economics and management.