Efficient Estimation and Model Selection for Grouped Data with Local Moments

Abstract

This paper proposes efficient estimation methods of unknown parameters when frequencies as well as local moments are available in grouped data. Assuming the original data is an i.i.d. sample from a parametric density with unknown parameters, we obtain the joint density of frequencies and local moments, and propose a maximum likelihood (ML) estimator. We further compare it with the generalized method of moments (GMM) estimator and prove these two estimators are asymptotically equivalent in the first order. Based on the ML method, we propose to use the Akaike information criterion (AIC) for model selection. Monte Carlo experiments show that the estimators perform remarkably well, and AIC selects the right model with high frequency.