A Re-regression Method For Bias-corrected Estimation Of Generalized Linear Model

The generalized linear models are widely used in economy, biology, medical science and other fields. However, with the increase of samples, especially when the dimension p is much larger than the sample number n, the traditional parameter estimation method can not choose a real model. In high dimensional statistical problems, we do variables selection of models through penalty, that is to compress those coefficients of useless variables trend to zero but retain the regression parameters which really work in the model.Think over the generalized linear models The Y obeys index distribution as followsThere are many methods to select the variables of this model:First.LASSOSecond,Dantzig selectorThird,Bridge Although these methods solve the difficulty of using super multi-variable to estimate the model,they all compress the significant variables. This deviation will be significantly increased with the increase of P.This paper studies the relation between the expectations of the parameter estimation and Penalty parameter. We discover three ways have a unified form in certain condition-s.We can see the unified form as shown below. Because of the unified form,we build up a new linear regression model.We conside βλk as Y and conside Aλk as X in linear regression model.Obviously, the constant in linear model is the true values of the parameters, we estimate it and we w-ould get another estimate values of parameters. The theorem and numerical simulation, can proved that this estimates can reduce the bias and variance.