Model-Free Feature Screening Based on Data Aggregation for Ultra-High-Dimensional Longitudinal Data

Ultra-high dimensional longitudinal data feature screening procedures are widely studied, but most require model assumptions. The screening performance of these methods may not be excellent if we specify an incorrect model. To resolve the above problem, a new model-free method is introduced where feature screening is performed by sample splitting and data aggregation. Distance correlation is used to measure the association at each time point separately, while longitudinal correlation is modeled by a specific cumulative distribution function to achieve efficiency. In addition, we extend this new method to handle situations where the predictors are correlated. Both methods possess excellent asymptotic properties and are capable of handling longitudinal data with unequal numbers of repeated measurements and unequal intervals between repeated measurement time points. Compared to other model-free methods, the two new methods are relatively insensitive to within-subject correlation, and they can help reduce the computational burden when applied to longitudinal data. Finally, we use some simulated and empirical examples to show that both new methods have better screening performance.