An Investigation Of Methods For Handling Missing Data With Adaptive Elastic-net Regression

Incomplete data is often found in real world statistical applications.In this paper,we extend the non-negative definite covariance approach under elastic-net proposed by Choi and Tibshirani(2013)to adaptive elastic-net.Also,this paper introduces a method for estimating the parameters which compensates for the missing observations.We first,derive an unbiased estimator of the objective function with respect to the missing data and then,modify the criterion to ensure convexity.Finally,we extend our approach to a family of models that embraces the mean imputation method.These approaches are compared to the mean imputation method,one of the simplest methods for dealing with missing observations problem,via simulations and calculating the mean square error of each method.Finally,we also investigate the model prediction effect of the non-negative covariance approach under the adaptive elastic-net regression model with the missing value problem by analyzing the real data of bike-sharing dataset and prostate cancer disease dataset.