Improved inference in generalized mean-reverting processes with multiple change-points

Nkurunziza, Sévérien; Fu, Kang

doi:10.1214/19-ejs1548

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…The minimization of (2.3) needs to be done numerically by using the dynamical programming algorithm which is similar to the one used in Nkurunziza and Fu (2019), Chen and Nkurunziza (2015) and references therein. For the convenience of the reader, we outline the algorithm in the Appendix D. In summary, in this section, we propose a tensor-response model with unknown number of changepoints.…”

Section: Estimation In the Case Of Unknown Change-pointsmentioning

confidence: 99%

Improved estimation in tensor regression with multiple change-points

Ghannam

Nkurunziza

2022

Electron. J. Statist.

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In this paper, we consider an estimation problem about the tensor coefficient in a tensor regression model with multiple and unknown change-points. We generalize some recent findings in five ways. First, the problem studied is more general than the one in context of a matrix parameter with multiple change-points. Second, we develop asymptotic results of the tensor estimators in the context of a tensor regression with unknown change-points. Third, we construct a class of shrinkage tensor estimators that encompasses the unrestricted estimator (UE) and the restricted estimator (RE). Fourth, we generalize some identities which are crucial in deriving the asymptotic distributional risk (ADR) of the tensor estimators. Fifth, we show that the proposed shrinkage estimators perform better than the UE. The additional novelty of the established results consists in the fact that the dependence structure of the errors is as weak as that of an L 2 -mixingale. Finally, the theoretical results are corroborated by the simulation findings and our methods are applied to analyse MRI and fMRI datasets.

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Section: Estimation In the Case Of Unknown Change-pointsmentioning

confidence: 99%