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Notes on M-Estimation in Exponential Signal Models

Communications in Mathematics and Statistics volume 9, pages 139–151 (2021)Cite this article

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.

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Authors and Affiliations

  1. School of Economics, Hefei University of Technology, Hefei, China

    Shu Ding

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Yuehua Wu

  3. Department of Mathematics, Portland State University, Portland, OR, USA

    Kwok-Wai Tam

Authors
  1. Shu Ding
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  2. Yuehua Wu
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  3. Kwok-Wai Tam
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Correspondence to Shu Ding.

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Ding, S., Wu, Y. & Tam , KW. Notes on M-Estimation in Exponential Signal Models. Commun. Math. Stat. 9, 139–151 (2021). https://doi.org/10.1007/s40304-019-00190-7

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  • DOI: https://doi.org/10.1007/s40304-019-00190-7

Keywords

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

Mathematics Subject Classification

  • 62H12