Monte Carlo local likelihood approximation.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Maximum Likelihood Estimation (MLE) is a fundamental statistical inference method.
• Bayesian methods offer an alternative by treating parameters as random variables.
• Existing methods for MLE approximation can be computationally intensive.

Purpose of the Study:

• To propose a novel method, Monte Carlo Local Likelihood (MCLL), for approximating MLE.
• To develop an efficient approach for computing standard errors and Bayes factors within the MCLL framework.
• To evaluate the performance of the MCLL method through empirical and simulation studies.

Main Methods:

• MCLL approximates MLE by treating model parameters as random variables and sampling from their posterior distribution.
• The likelihood function is approximated by fitting a density to posterior samples and adjusting by the prior density.
• Posterior density estimation is performed using local likelihood density estimation, approximating the log-density with local polynomial functions.

Main Results:

• The MCLL method provides a viable approximation to MLE.
• The developed technique allows for efficient computation of standard errors and Bayes factors.
• Empirical and simulation studies confirm the effectiveness of the MCLL approach.

Conclusions:

• MCLL offers a powerful new tool for approximating maximum likelihood estimation.
• The method facilitates efficient calculation of key statistical measures like standard errors and Bayes factors.
• MCLL shows promise for various statistical modeling and inference applications.