Transfer Learning for Error-Contaminated Poisson Regression Models

Poisson regression model has been a popular approach to characterize the count response and the covariates. With the rapid development of data collections, the additional source information can be easily recorded. To efficiently use the source data to improve the estimation under the original data, the transfer learning method is considered a strategy. However, challenging issues from the given datasets include measurement error and high-dimensionality in variables, which are not well explored in the context of transfer learning. In this paper, we propose a novel strategy to handle error-prone count responses and estimate the parameters in measurement error models by using the source data, and then employ the transfer learning method to derive the corrected estimator. Moreover, to improve the prediction and avoid the model uncertainty, we further establish the model averaging strategy. Simulation and breast cancer data studies verify the satisfactory performance of the proposed method and the validity of handling measurement error.