Statistical Inference And Application For Two Types Of Models

This dissertation stydies the robust estimation and variable selection in a high-dimensional threshold model and a class of Box-Cox transformation models for multipe type recurrence event data.The threshold model has been widely used in economics,finance and other fields.Depending on whether the value of the threshold variable exceeds a certain thresh-old,the data can be split into several classes for analyzing.The threshold regression model provides an effective way to study the nonlinear relationship by splitting the samples into subsamples.With the advancement of technology,large volumes of high-dimensional data bring challenges to modern statistics.Penalized regression methods have becomed a popular approach to achieve variable selection in recent years.Mean-while,the corresponding penalized regression mehtods based on the quadratic loss func-tion for the theshold model have also been studied in the statistical literature.However,we all know that the quadratic loss function is sensitive to outliers and heavy-tailed er-rors.First,we propose an approach to combine the robust criteria and the lasso penalty together for the high-dimensional threshold model.Our proposed approach is able to robustly estimate the regression coefficients as well as the threshold parameter and perform variable selection simultaneously.Second,we consider variable selection at the group level instead of individual covariate level for the high-dimensional threshold model.We use the group lasso penalty to replace the lasso penalty.In other words,we combine the robust criteria and the group lasso penalty together for the high-dimensional threshold model.As a result,our new approach could perform group variable and obtain roubust estimation.In medical research,the event of interest may occur more than once for a given participant,and such results are called recurrent events.The Box-Cox transformation models are frequently used to analyze recurrent event data.If there are multiple types of events of interest in a clinical study,and these results may occur repeatedly during the observation period.Such results are called multiple type recurrent events,which are commonly encountered in reality.Finally,we propose a class of Box-Cox trans-formation models for multiple type recurrent event data,which is an extension of the Box-Cox transformation models for recurrent event data,and make statistical inference on the proposed models.