A linear regression model with persistent level shifts: An alternative to infill asymptotics

Woody, Jonathan; Lund, Robert

doi:10.1016/j.spl.2014.08.018

Cited by 3 publications

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“…In the context of the existence of some changepoints, ignoring them may lead to wrong statistical conclusions. For some references about change-point problems and related issues, we quote for example Qu and Perron (2007), Gombay (2010), Robbins et al (2011), Gallagher et al (2012), Woody and Lund (2014), Chen and Nkurunziza (2015), Chen and Nkurunziza (2016), Roy et al (2017), and references therein. The restriction studied is especially useful for taking into account some prior knowledge about the tensor predictor and/or for testing the statistical significance of some coefficients.…”

Section: Introductionmentioning

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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