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Super efficient frequency estimation |
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| Authors: | Debasis Kundu Swagata Nandi Li Bai |
| Affiliation: | a Department of Mathematics and Statistics, Indian Institute of Technology Kanpur 208016, India b KLASMOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, PR China c Department of Statistics and Applied Probability, The National University of Singapore, Singapore 117546, Singapore d Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India e Department of Electrical and Computer Engineering, College of Engineering, Temple University, USA |
| Abstract: | In this paper we propose a modified Newton-Raphson method to obtain super efficient estimators of the frequencies of a sinusoidal signal in presence of stationary noise. It is observed that if we start from an initial estimator with convergence rate Op(n−1) and use Newton-Raphson algorithm with proper step factor modification, then it produces super efficient frequency estimator in the sense that its asymptotic variance is lower than the asymptotic variance of the corresponding least squares estimator. The proposed frequency estimator is consistent and it has the same rate of convergence, namely Op(n−3/2), as the least squares estimator. Monte Carlo simulations are performed to observe the performance of the proposed estimator for different sample sizes and for different models. The results are quite satisfactory. One real data set has been analyzed for illustrative purpose. |
| Keywords: | Sinusoidal signals Least squares estimators Asymptotic distributions Modified Newton-Raphson |
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