Maximum likelihood estimation under efficient importance sampling for non-linear state space models

Abstract

The interest of this dissertation lays on the Likelihood Evaluation and Maximum Likelihood (ML) Parameter Estimation on the Non-linear State Space Model in which the analytical solution is not available. An algorithm known as Efficient Importance Sampling (EIS) is adopted for the continuous approximation of likelihood function and we proposed amethod to further improve its performance by accomplishing a more precise calculation on the weight functions. With respect to the ML parameter estimation, we proposed a Monte Carlo EM algorithm based on EIS procedure and Constant-Weight principle to achieve lower computational complexity and better performance on parameter estimation in comparison with algorithms based on Particle Filters. Moreover, by paying a small price on the estimation performance, we further developed a technique known as Fast-Sampling for our proposed EIS-based EM algorithm to realize more computational efficiency gain. Finally, we illustrate these developed algorithm and technique in applications to the Dynamic Stochastic General Equilibrium modeling which is a very popular methodology designed for Macroeconomics analysis.