Estimating the fundamental frequency using modified Newton–Raphson algorithm. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Nandi, Swagata; Kundu, Debasis
• Is Part Of: Statistics. Volume 53:Issue 2(2019)
• Page Start: 440
• Page End: 458
• Publication Date: 2019-03-04
• Subjects: Fundamental frequency model -- approximate least squares estimator -- modified Newton–Raphson algorithm -- super efficient estimator; 62J02 -- 62E20 -- 62C05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1552962
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In this paper, we propose a modified Newton–Raphson (NR) algorithm to estimate the frequency parameter in the fundamental frequency model in presence of an additive stationary error. The proposed estimator is super efficient in nature in the sense that its asymptotic variance is less than the asymptotic variance of the least squares estimator. With a proper step factor modification, the proposed modified NR algorithm produces an estimator with the rateO p ( n − ( 3 / 2 ) ), the same rate as the least squares estimator. Numerical experiments are performed for different sample sizes, different error variances and for different models. For illustrative purposes, two real data sets are analysed using the fundamental frequency model and the estimators are obtained using the proposed algorithm. It is observed that the model and the proposed algorithm work quite well in both cases.