M-test in linear models with negatively superadditive dependent errors

Yuncai Yu; Hongchang Hu; Ling Liu; Shouyou Huang

doi:10.1186/s13660-017-1509-6

M-test in linear models with negatively superadditive dependent errors

J Inequal Appl. 2017;2017(1):235. doi: 10.1186/s13660-017-1509-6. Epub 2017 Sep 22.

Authors

Yuncai Yu¹, Hongchang Hu², Ling Liu³, Shouyou Huang²

Affiliations

¹ State Key Laboratory of Mechanics and Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 China.
² Department of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002 China.
³ Department of Information Science and Technology, Donghua University, Shanghai, 201600 China.

Abstract

This paper is concerned with the testing hypotheses of regression parameters in linear models in which errors are negatively superadditive dependent (NSD). A robust M-test base on M-criterion is proposed. The asymptotic distribution of the test statistic is obtained and the consistent estimates of the redundancy parameters involved in the asymptotic distribution are established. Finally, some Monte Carlo simulations are given to substantiate the stability of the parameter estimates and the power of the test, for various choices of M-methods, explanatory variables and different sample sizes.

Keywords: M-test; Monte Carlo simulations; NSD random sequences; asymptotic property; linear regression models.