The Sequential estimation of generalized linear model coefficients

Generalized LinearModels (GLM) allows us to model the relationship between a response variable and one or more predictor variables while taking into account the distribution of the response variable. It is a useful tool for modeling data that do not follow a normal distribution and can be applied to a wide range of data types and problem settings. As data becomes increasingly relevant in our daily lives, the use of these models is becoming more important. However, this increase in importance also implies an increase in the complexity of estimation due to the volume of data that must be processed. In contrast, when dealing with laboratory experiments or other situations, we may have limited observations making it challenging to obtain robust estimates. To address these challenges, this paper proposes a simple and efficient method for estimating the coefficients of GLM and provides mathematical proof for the almost sure convergence of this method towards the desired solution. The proposed method is also validated on real-world data, reinforcing its utility and effectiveness.