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A change-point estimator using local Fourier series

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  • Jaehee Kim
  • Jeffrey Hart

Abstract

In this paper, we propose a change-point estimator based on local Fourier series estimates. At each potential change point, two Fourier series estimates are computed, one using data to the left of the possible change point and the other using data to the right. The difference between these estimates is computed, and the change-point estimate is defined to be the point at which this absolute difference is maximised. Mean-squared error properties of our local series estimates are derived and the change-point estimator is shown to converege to the truth at rate n−1 (where n is the sample size). In a simulation study, the proposed change-point estimator has a better overall performance than a local linear method. A data-driven bandwidth selector is also proposed and applied to the classical Nile River data.

Suggested Citation

  • Jaehee Kim & Jeffrey Hart, 2011. "A change-point estimator using local Fourier series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 83-98.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:83-98
    DOI: 10.1080/10485251003721232
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    Cited by:

    1. Helida Nurcahayani & I Nyoman Budiantara & Ismaini Zain, 2021. "The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression," Mathematics, MDPI, vol. 9(10), pages 1-22, May.

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