Consistency of M-estimators of nonlinear signal processing models

详细信息    查看全文

• 作者：Kaushik Mahata^a ; Amit Mitra^b ; ^{amitra@iitk.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Sharmishtha Mitra^b
• 关键词：Asymptotic analysis ; M-estimator ; Nonlinear signal processing model ; Robust statistics ; Strong consistency
• 刊名：Statistical Methodology
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：28
• 期：Complete
• 页码：18-36
• 全文大小：761 K

文摘

In this paper, we consider the problem of robust M-estimation of parameters of nonlinear signal processing models. We investigate the conditions under which estimators are strongly consistent for convex and non-convex penalty functions and a wide class of noise scenarios, contaminating the actual transmitted signal. It is shown that the M-estimators of a general nonlinear signal model are asymptotically consistent with probability one under different sets of sufficient conditions on loss function and noise distribution. Simulations are performed for nonlinear superimposed sinusoidal model to observe the small sample performance of the M-estimators for various heavy tailed error distributions, outlier contamination levels and sample sizes.