Monte Carlo local likelihood approximation

We propose the Monte Carlo local likelihood (MCLL) method for approximating maximum likelihood estimation (MLE). MCLL initially treats model parameters as random variables, sampling them from the posterior distribution as in a Bayesian model. The likelihood function is then approximated up to a constant by fitting a density to the posterior samples and dividing the approximate posterior density by the prior. In the MCLL algorithm, the posterior density is estimated using local likelihood density estimation, in which the log-density is locally approximated by a polynomial function. We also develop a new method that allows users to efficiently compute standard errors and the Bayes factor. Two empirical and three simulation studies are provided to demonstrate the performance of the MCLL method.