Post Selection Estimation and Prediction in Poisson Regression Model

Abstract

The use of subspace information for estimating parameters of the model has gained increasing attention in recent years. However, the quality of the subspace information is usually unknown, and in consequence the classical maximum likelihood estimation strategies, which rely on this information, become biased and inefficient. Our goal was to improve the performance of estimation strategies for a Poisson regression model for which subspace information is available. We proposed estimators based on the linear shrinkage, preliminary test, and Stein-type strategies and investigated their asymptotic properties using the notation of asymptotic distributional bias and risk. Comprehensive Monte Carlo simulations were conducted to assess the simulated relative efficiency of the proposed estimators. Further, comparisons were made with the two penalized likelihood estimators: least absolute shrinkage and selection operator (LASSO) and ridge. Finally, the proposed estimators were applied to a real data set, to confirm their usefulness. Based on our findings, the proposed estimators were more efficient than the classical estimator when the accuracy of the subspace information was unknown.