Feature Screening For Ultra-High Dimensional Heterogeneous Data And Competing Risks Data

Feature screening has become a popular topic of statistical research in recent years because it may quickly reduce the dimensionality of variables from ultra-high to an acceptable range,allowing for successful statistical inference.In practice,as dimensionality grows,data complexity grows as well,manifesting itself in heterogeneity,multi-response,joint dependence,and interaction.Furthermore,because ultra-high dimensional data is common in biology and finance,the censoring that follows will further complicate the data.Moreover,throughout the follow-up studies,the subjects may encounter a variety of failure events,making feature screening more challenging.In this case,the complex characteristics of data in screening investigations must be taken into account.As a result,this thesis presents two separate feature screening approaches for different types of complicated data,both based on the idea of marginal and non-marginal feature screening.The following are the specific studies.(1)We develop a robust feature screening approach based on the distance correlation coefficient for ultra-high dimensional heterogeneous and multi-response data.This method is model-free,homogeneity-insensitive,and may be used to multivariate response variables.Furthermore,by reducing the correlation between covariates,an effective iterative approach is proposed to cope with joint dependence.Without requiring the responses or predictors to satisfy the subexponential tail,we also establish the sure screening feature.This method outperforms certain existing approaches based on numerical comparisons and real data applications.(2)For ultra-high dimensional competing risks data,we consider the interaction between the exposure variable(e.g.,time,spatial location,etc.)and covariates,then propose a non-marginal feature screening procedure based on varying coefficient competing risks model,and the approximation of the likelihood function is obtained by Taylor expansion.After that,the L0 sparse constraint estimates are obtained using the projected gradient descent algorithm.The proposed screening method is shown to enjoy the sure screening property.We finally illustrates the superior empirical performance of the proposed method by simulation examples and real data applications.