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Estimation of the number of spikes, possibly equal, in the high-dimensional case

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  • Passemier, Damien
  • Yao, Jianfeng

Abstract

Estimating the number of spikes in a spiked model is an important problem in many areas such as signal processing. Most of the classical approaches assume a large sample size n whereas the dimension p of the observations is kept small. In this paper, we consider the case of high dimension, where p is large compared to n. The approach is based on recent results of random matrix theory. We extend our previous results to a more difficult situation where some spikes are equal, and compare our algorithm to an existing benchmark method.

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  • Passemier, Damien & Yao, Jianfeng, 2014. "Estimation of the number of spikes, possibly equal, in the high-dimensional case," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 173-183.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:173-183
    DOI: 10.1016/j.jmva.2014.02.017
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    References listed on IDEAS

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    Cited by:

    1. Forzani, Liliana & Gieco, Antonella & Tolmasky, Carlos, 2017. "Likelihood ratio test for partial sphericity in high and ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 18-38.
    2. Shen, Keren & Yao, Jianfeng & Li, Wai Keung, 2019. "On a spiked model for large volatility matrix estimation from noisy high-frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 207-221.
    3. Zeng, Yicheng & Zhu, Lixing, 2023. "Order determination for spiked-type models with a divergent number of spikes," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. Passemier, Damien & McKay, Matthew R. & Chen, Yang, 2015. "Hypergeometric functions of matrix arguments and linear statistics of multi-spiked Hermitian matrix models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 124-146.

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