Simulation Analysis of Asymptotic Normality of Maximum Likelihood Estimation Based on the Fisher Scoring Algorithm in Generalized Poisson Regression Modeling

Abstract

Maximum Likelihood Estimation (MLE) is a method widely used in statistics to estimate the parameters of statistical models. One of the critical aspects of MLE is its asymptotic properties, especially its asymptotic normality. Asymptotic normality refers to the property where the MLE distribution approaches a normal distribution as the sample size tends to infinity. Meanwhile, Fisher Scoring Algorithm (FSA) stands out as a versatile and efficient tool for parameter estimation in various models and statistical disciplines. This research was conducted to obtain the distribution of the MLE estimator based on the FSA. The simulation study used the Bootstrap Method in the Generalized Poisson Regression Model with 600, 700, 800, 900, and 1000 repetitions. The simulation results show that the MLE estimator based on the FSA has the same distribution as the classical MLE estimator; namely, a Normal distribution.