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On Weighted Least Squares Estimators for Chirp Like Model

Author

Listed:
  • Debasis Kundu

    (Department of Mathematics and Statistics, Indian Institute of Technology Kanpur)

  • Swagata Nandi

    (Theoretical Statistics and Mathematics Unit, Indian Statistical Institute)

  • Rhythm Grover

    (Mehta Family School of Data Science and Artificial Intelligence, IIT Guwahati)

Abstract

In this paper we have considered the chirp like model which has been recently introduced, and it has a very close resemblance with a chirp model. We consider the weighted least squares estimators of the parameters of a chirp like model in presence of an additive stationary error, and study their properties. It is observed that although the least squares method seems to be a natural choice to estimate the unknown parameters of a chirp like model, the least squares estimators are very sensitive to the outliers. It is observed that the weighted least squares estimators are quite robust in this respect. The weighted least squares estimators are consistent and they have the same rate of convergence as the least squares estimators. We have further extended the results in case of multicomponent chirp like model. Some simulations have been performed to show the effectiveness of the proposed method. In simulation studies, weighted least squares estimators have been compared with the least absolute deviation estimators which, in general, are known to work well in presence of outliers. One EEG data set has been analyzed and the results are quite satisfactory.

Suggested Citation

  • Debasis Kundu & Swagata Nandi & Rhythm Grover, 2024. "On Weighted Least Squares Estimators for Chirp Like Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 27-66, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00313-x
    DOI: 10.1007/s13171-023-00313-x
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    References listed on IDEAS

    as
    1. Lahiri, Ananya & Kundu, Debasis & Mitra, Amit, 2015. "Estimating the parameters of multiple chirp signals," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 189-206.
    2. Hugues Guillet de Chatellus & Luis Romero Cortés & Côme Schnébelin & Maurizio Burla & José Azaña, 2018. "Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
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