One-step Statistical Estimation Method for Generalized Linear Models

In this article, the one-step estimation procedure is presented for generalized linear models. In these models, the maximum likelihood estimator, which is asymptotically efficient, has no closed-form and gradient-descent methods are generally used for its numerical computation. Nevertheless, when the amount of data is large and/or the number of explanatory variables is high, then the computations can be very consuming. To overcome this difficulty, the one-step estimation procedure is used, which is based on an initial (inefficient) guess estimator and a single step of the Fisher scoring. The main advantage of this procedure is that only one iterative step is required to achieve the asymptotic efficiency. The results are validated numerically by means of Monte-Carlo simulations.The estimation procedure is used to fit generalized linear models for climate risk insurance data.