Exponential Series Estimator of multivariate densities

摘要

We present an Exponential Series Estimator (ESE) of multivariate densities, which has an appealing information-theoretic interpretation. For a d dimensional random variable x with density po, the ESE takesthe form P_o(x)) = exp (sum from i=0 to m1 of (...) theta_i phi_i) where phi are some real-valued, linearly independent functions defined on the support of po. We derive the convergence rate of the ESE in terms of the Kullback-Leibler Information Criterion, the integrated squared error and some other metrics. We also derive its almost sure uniform convergence rate. We then establish the asymptotic normality of We undertake two sets of Monte Carlo experiments. The first experiment examines the ESE performance using mixtures of multivariate normal densities. The second estimates copula density functions. The results demonstrate the efficacy of the ESE. An empirical application on the joint distributions of stock returns is presented.