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The LASSO has been widely studied and used in many applications, but it not shown oracle properties. Depending on a consistent initial parameters vector, an adaptive LASSO showed oracle properties, which it is consistent in variable selection and asymptotically normal in coefficient estimation. In Poisson regression model, the usual adaptive LASSO using maximum likelihood coefficient estimators can result in very poor performance when there is multicollinearity. In this study, we proposed an adjusting of the adaptive LASSO to take into account the maximum likelihood standard errors of the coefficient parameters. The performance of the adaptive LASSO was demonstrated through simulation and real data. Our simulation and real data results show that adaptive LASSO has advantage in terms of both prediction and variable selection comparing with other existing adaptive penalized methods when the explanatory variables are highly correlated. Hence we can conclude that adaptive LASSO is a reliable adaptive penalized method in a Poisson regression model.

Adjusted Adaptive LASSO in High-dimensional Poisson Regression Model