The article introduces a new statistical method called h-likelihood, which is a modified version of the widely used maximum likelihood estimation. By maximizing the h-likelihood, researchers can obtain optimal estimators for different types of statistical models with random parameters. This method allows for efficient estimation of both fixed and random parameters, achieving a lower bound on estimation accuracy. The researchers also explore scenarios where the estimation process may not be consistent and provide insights on how to handle such situations. Overall, h-likelihood offers a powerful tool for statistical inference in a wide range of models.