Alternating Projection Algorithm in Maximum Likelihood Estimation with MATLAB Implementation

In this paper, we present a detailed examination of the alternating projection algorithm within maximum likelihood estimation framework. This algorithm serves as a powerful parameter estimation method that operates by maximizing the likelihood function of probabilistic models. The implementation involves iterative projection operations between constraint sets, where each iteration alternates between projecting onto different feasible regions to converge toward optimal parameter values. Our discussion includes not only thorough algorithmic explanations but also provides complete MATLAB simulation source code to facilitate better understanding and practical application. The code demonstrates key implementation aspects such as: - Initialization of parameter estimates - Iterative projection operations between constraint sets - Convergence criteria checking - Likelihood function optimization We are confident that through studying this material, you will gain deeper insights into both theoretical foundations and practical implementation of this algorithm, enabling effective application in various statistical estimation scenarios. The MATLAB code incorporates efficient matrix operations and optimization techniques, featuring functions for probability model specification, projection computations, and convergence monitoring to ensure robust performance across different estimation problems.