Residual empirical processes and their application to GM-testing for the autoregression order

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• 作者：D. M. Esaulov (1)
  
• 关键词：hypotheses testing ; autoregression ; generalized M ; tests ; robustness ; outliers ; residual empirical processes ; primary 62M10 ; secondary 62G10 ; 62G20
• 刊名：Mathematical Methods of Statistics
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：22
• 期：4
• 页码：333-349
• 全文大小：739 KB
• 作者单位：D. M. Esaulov (1)
  
  1. Dept. of Mech. and Math., Moscow State Univ., Moscow, Russia
  
• ISSN：1934-8045

文摘

In the paper a new nonparametric generalized M-test for hypotheses about the order of linear autoregression AR(p) is constructed. We also establish robustness of this test in the model of data contamination by independent additive outliers with intensity O(n ?/2). Robustness is formulated in terms of limiting power equicontinuity. Test statistics are constructed with the help of residual empirical processes. We establish the asymptotic uniform linearity of these processes in the defined contamination model.