Single-index modal regression via outer product gradients

Yang，Jing1; Tian，Guoliang2; Lu，Fang1; Lu，Xuewen3

2020-04-01

10.1016/j.csda.2019.106867

COMPUTATIONAL STATISTICS & DATA ANALYSIS   影响因子和分区

0167-9473

1872-7352

Most existing methods for single-index models (SIM) were focused on either mean regression or quantile regression, while the former is sensitive to outliers or heavy tailed distributions and the latter may lose efficiency for normally distributed data. Then a robust, efficient and easily implemented estimation procedure for index coefficient in SIM is developed by integrating the ideas of local modal regression and outer product gradients. Under some mild conditions, we establish the asymptotic normality of the proposed estimators. We further discuss the optimal choices of tuning parameters including one common bandwidth for nonparametric polynomial smoothing and another key bandwidth that controls the robustness and efficiency of the estimator, based on the derived theories. A practical modified EM algorithm is also presented for implementation. Finally, some simulation studies and two real data analysis are conducted to confirm the merits and theoretical findings of the novel method.

Asymptotic properties Local modal regression Outer product gradients Robustness Single-index models

EI ; SCI ; SSCI

英语

其他

National Natural Science Foundation of China[11771199] ; National Natural Science Foundation of China[11801168] ; National Natural Science Foundation of China[11801169] ; Scientific Research Foundation of Hunan Provincial Education Department[18B024] ; Natural Science Foundation of Hunan Province[2018JJ3322] ; Natural Science Foundation of Hunan Province[2019JJ50378] ; Natural Sciences and Engineering Research Council of Canada[RG/PIN261567-2013]

Computer Science ; Mathematics

Computer Science, Interdisciplinary Applications ; Statistics & Probability

WOS:000515446200002

Elsevier B.V.

20194207555521

Bandwidth ; Efficiency ; Normal distribution ; Robustness (control systems)

Information Theory and Signal Processing:716.1 ; Control Systems:731.1 ; Production Engineering:913.1 ; Probability Theory:922.1 ; Mathematical Statistics:922.2

MATHEMATICS

2-s2.0-85073353671

Scopus

1.Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education)College of Mathematics and StatisticsHunan Normal University,Changsha,410081,China
2.Department of Statistics and Data ScienceSouthern University of Science and Technology,Shenzhen,518055,China
3.Department of Mathematics and StatisticsUniversity of CalgaryCalgary,AB,T2N 1N4,Canada

Yang，Jing,Tian，Guoliang,Lu，Fang,et al. Single-index modal regression via outer product gradients[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2020,144.

Yang，Jing,Tian，Guoliang,Lu，Fang,&Lu，Xuewen.(2020).Single-index modal regression via outer product gradients.COMPUTATIONAL STATISTICS & DATA ANALYSIS,144.

Yang，Jing,et al."Single-index modal regression via outer product gradients".COMPUTATIONAL STATISTICS & DATA ANALYSIS 144(2020).