Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms |
| |
Authors: | Maria P. Braun Simos G. Meintanis Viatcheslav B. Melas |
| |
Affiliation: | 1. Faculty of Mathematics and Mechanics, St. Petersburg State University, 28 University Avenue, Petrodvoretz, 198504 St. Petersburg, Russia;2. Department of Economics, National and Kapodistrian University of Athens, 8 Pesmazoglou Street, 105 59 Athens, Greece E‐mail: simosmei@eccon.uoa.gr |
| |
Abstract: | Parameter estimation based on the generalized method of moments (GMM) is proposed. The proposed method employs a distance between an empirical and the corresponding theoretical transform. Estimation by the empirical characteristic function (CF) is a typical example, but alternative empirical transforms are also employed, such as the empirical Laplace transform when dealing with non‐negative random variables. D‐optimal designs are discussed, whereby the arguments of the empirical transform are chosen by maximizing the determinant of the asymptotic Fisher information matrix for the resulting estimators. The methods are applied to some parametric models for which classical inference is complicated. |
| |
Keywords: | Empirical characteristic function empirical Laplace transform parameter estimation normal inverse Gaussian model normal variance Gamma model |
|
|