Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression model.The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases.The slope function is fitted by B-spline.Under suitable conditions,the authors obtain the convergence rates and asymptotic normality of the estimators.Finally,simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method.Both the simulation results and the real data analysis confirm that the newly proposed method works very well.

Distributed Penalized Modal Regression for Massive Data

Nowadays,researchers are frequently confronted with challenges from massive data computing by a number of limitations of computer primary memory.Modal regression(MR)is a good alternative of the mean regression and likelihood based methods,because of its robustness and high efficiency.To this end,the authors extend MR to massive data analysis and propose a computationally and statistically efficient divide and conquer MR method(DC-MR).The major novelty of this method consists of splitting one entire dataset into several blocks,implementing the MR method on data in each block,and deriving final results through combining these regression results via a weighted average,which provides approximate estimates of regression results on the entire dataset.The proposed method significantly reduces the required amount of primary memory,and the resulting estimator is theoretically as efficient as the traditional MR on the entire data set.The authors also investigate a multiple hypothesis testing variable selection approach to select significant parametric components and prove the approach possessing the oracle property.In addition,the authors propose a practical modified modal expectation-maximization(MEM)algorithm for the proposed procedures.Numerical studies on simulated and real datasets are conducted to assess and showcase the practical and effective performance of our proposed methods.