Bahadur representations of M-estimators and their applications in general linear models.
JOURNAL OF INEQUALITIES AND APPLICATIONS 2018;
2018:123. [PMID:
30137866 PMCID:
PMC5978921 DOI:
10.1186/s13660-018-1715-x]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Accepted: 05/11/2018] [Indexed: 06/08/2023]
Abstract
Consider the linear regression model yi=xiTβ+ei,i=1,2,…,n, where ei=g(…,εi-1,εi) are general dependence errors. The Bahadur representations of M-estimators of the parameter β are given, by which asymptotically the theory of M-estimation in linear regression models is unified. As applications, the normal distributions and the rates of strong convergence are investigated, while {εi,i∈Z} are m-dependent, and the martingale difference and (ε,ψ) -weakly dependent.
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