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.

PDF
Communications in Mathematics and Statistics ›› 2021, Vol. 9 ›› Issue (2) : 139 -151. DOI: 10.1007/s40304-019-00190-7
Article

Notes on M-Estimation in Exponential Signal Models

Author information +
History +
PDF

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

Cite this article

Download citation ▾
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

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Bai ZD, Wu YH. Recursive algorithm for M-estimation of regression coefficients and scatter parameters in linear models. Indian J. Stat.. 1993, 55 2 199-218

[2]

Bai ZD, Wu Y. General M-estimation. J. Multivar. Anal.. 1997, 63 1 119-135

[3]

Englund JE. Multivariate recursive M-estimations of location and scatter for dependent sequences. J. Multivar. Anal.. 1993, 45 2 257-273

[4]

Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust Statistics—The Approach Based on Influence Functions. 1986 New York: Wiley

[5]

Miao BQ, Wu Y. Limiting behavior of recursive M-estimators in multivariate linear regression models. J. Multivar. Anal.. 1996, 59 1 60-80

[6]

Miao BQ, Tong Q, Wu YH, Jin BS. Selecting an adaptive sequence for computing recursive m-estimators in multivariate linear regression models. J. Syst. Sci. Complex.. 2013, 26 4 583-594

[7]

Miao BQ, Wu YH, Liu DH, Tong Q. Asymptotic normality of the recursive m-estimators of the scale parameters. Ann. Inst. Stat. Math.. 2007, 59 2 367-384

[8]

Oh, S.G., Kashyap, R.L.: Robust frequency estimation. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2132–2135 (1989)

[9]

Rao CR, Wu YH. A note on constrained M-estimation and its recursive analog in multivariate linear regression models. Sci. China Ser. A Math.. 2009, 52 6 1235-1250

[10]

Wu YH, Tam KW. $M$-estimation in exponential signal models. IEEE Trans. Signal Process.. 2001, 49 2 373-380

AI Summary AI Mindmap
PDF

153

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/