Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jspi.2011.02.006
Title: Super efficient frequency estimation
Authors: Kundu, D.
Bai, Z. 
Nandi, S.
Bai, L.
Keywords: Asymptotic distributions
Least squares estimators
Modified Newton-Raphson
Sinusoidal signals
Issue Date: Aug-2011
Citation: Kundu, D., Bai, Z., Nandi, S., Bai, L. (2011-08). Super efficient frequency estimation. Journal of Statistical Planning and Inference 141 (8) : 2576-2588. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jspi.2011.02.006
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. © 2011 Elsevier B.V.
Source Title: Journal of Statistical Planning and Inference
URI: http://scholarbank.nus.edu.sg/handle/10635/105397
ISSN: 03783758
DOI: 10.1016/j.jspi.2011.02.006
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