Theoretical Statistics and Mathematics Unit, ISI Delhi

Super Efficient Frequency Estimation

by Debasis Kundu, Zhidong Bai, Swagata Nandi and Li Bai

In this paper we propose a modified Newton-Raphson method to obtain super efficient
frequency estimators of sinusoidal signals in presence of stationary noise. It is
observed that if we start from an initial estimator with convergence rate
$O_p(n^{-1})$ and use the Newton-Raphson
algorithm with proper step factor modification, then it produces
super efficient frequency estimator in the sense it has asymptotic variance which is lower
than the asymptotic variance of the least squares estimator. The proposed frequency
estimator is consistent and have the optimum rate of convergence, namely $O_p(n^{-\frac{3}{2}})$,
which is same as the least squares estimator. Monte Carlo simulations are performed to observe
the performances 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.

isid/ms/2008/02 [fulltext]

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