Notes on M-Estimation in Exponential Signal Models

Shu Ding , Yuehua Wu , Kwok-Wai Tam

Communications in Mathematics and Statistics ›› 2021, Vol. 9 ›› Issue (2) : 139 -151.

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Communications in Mathematics and Statistics ›› 2021, Vol. 9 ›› Issue (2) : 139 -151. DOI: 10.1007/s40304-019-00190-7
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Notes on M-Estimation in Exponential Signal Models

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Abstract

An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam (IEEE Trans Signal Process 49(2):373–380, 2001), and the estimation was shown to be consistent under mild assumptions. In this paper, the limiting distributions of the M-estimators are investigated. It is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam (IEEE Trans Signal Process 49(2):373–380, 2001). In addition, a recursive algorithm for computing the M-estimators of frequencies is proposed, and the strong consistency of these estimators is established. Monte Carlo simulation studies using Huber’s $\rho $ function are also provided.

Keywords

Exponential signal model / M-estimation / Limiting distribution / Recursive algorithm / Consistency

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Shu Ding,Yuehua Wu,Kwok-Wai Tam. Notes on M-Estimation in Exponential Signal Models. Communications in Mathematics and Statistics, 2021, 9(2): 139-151 DOI:10.1007/s40304-019-00190-7

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