Application Of Random Weighting Method In Parameter Estimation Of Generalized Linear Models

Abstract:Linear statistical model is a very important statistical model, which includes the linear regression model, analysis of variance model and many other widely used models, on the second hand the theory and method of the linear model is the foundation to study other statistical models. However, the linear model also has some disadvan-tages, for example, it applies only in the case of continuous dependent variable y which means it does not apply to classified data. Besides, the strict linear relationship between x and y also makes the application field relatively narrow. To solve these three prob-lems, Nelder and Wedderburn put forward the generalized linear models which greatly widened the application field of the linear model in1972.When we solve the asymptotic distribution of parameter estimation of the gen-eralized linear model, the normal approximation method to calculate the asymptotic variance relates to the density function of variable y, which is generally unknown. To estimate the density function of y is very hard and easily causes errors. Randomly weighted method use the asymptotic distribution of random weighted estimation to ap-proximate the asymptotic distribution of original parameter estimation, bypassing the solving of the density function of y, so that the calculation of the parameter estimation is more accurate.In this paper, we proved the feasibility and applicability of the the randomly weighted method to solve the asymptotic variance of parameter estimation by theory demonstration and data simulation.