Theoretical Statistics and Mathematics Unit, ISI Delhi

Estimating the fundamental frequency using modified Newton-Raphson algorithm

by Swagata Nandi and Debasis Kundu

In this paper, we propose a modified Newton-Raphson algorithm to estimate the frequency parameter in the fundamental frequency model in presence of additive stationary error. The proposed estimator is super efficient in nature in the sense that its asymptotic variance is less than that of the least squares estimator having the same rate of convergence as the least squares estimator. With a proper step factor modification, we start Newton-Raphson algorithm with an initial estimator of order $O_p(n^{-1})$ and obtain an estimator with rate $O_p(n^{-\frac{3}{2}})$, the same rate as the least squares estimator. Numerical experiments are performed for different sample sizes, different error variances and different models. Three real datasets are analyzed using fundamental frequency model where the estimators are obtained using the proposed algorithm.

isid/ms/2016/08 [fulltext]

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