Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach

Dette, Holger; Kokot, Kevin

doi:10.1007/s10463-021-00795-2

Cited by 8 publications

(1 citation statement)

References 33 publications

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“…Avanesov and Buzun (2018) and Zhong et al (2019) studied the problem of change point detection of covariance matrix in a high‐dimensional setting. Dette and Kokot (2022) proposed a sup‐norm approach. Aston and Kirch (2012b), Gromenko et al (2017), and Stoehr et al (2021) studied the structural break problem for bivariate or trivariate functions, specifically, spatial‐temporal data and fMRI data.…”

Section: Introductionmentioning

confidence: 99%

Break point detection for functional covariance

Jiao

Frostig

Ombao

2022

Scandinavian J Statistics

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Many neuroscience experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero‐mean functional data. When there are structural breaks in higher‐order moments, it is not always easy to spot these by mere visual inspection. Motivated by this challenging problem in brain signal analysis, we propose a detection and testing procedure to find the change point in functional covariance. The detection procedure is based on the cumulative sum statistics (CUSUM). The fully functional testing procedure relies on a null distribution which depends on infinitely many unknown parameters, though in practice only a finite number of these parameters can be included for the hypothesis test of the existence of change point. This paper provides some theoretical insights on the influence of the number of parameters. Meanwhile, the asymptotic properties of the estimated change point are developed. The effectiveness of the proposed method is numerically validated in simulation studies and an application to investigate changes in rat brain signals following an experimentally‐induced stroke.

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Section: Introductionmentioning

confidence: 99%

Break point detection for functional covariance

Jiao

Frostig

Ombao

2022

Scandinavian J Statistics

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A test for heteroscedasticity in functional linear models

Cameron

Bagchi

2021

TEST

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We propose a new test to validate the assumption of homoscedasticity in a functional linear model. We consider a minimum distance measure of heteroscedasticity in functional data, which is zero in the case where the variance is constant and positive otherwise. We derive an explicit form of the measure, propose an estimator for the quantity, and show that an appropriately standardized version of the estimator is asymptotically normally distributed under both the null (homoscedasticity) and alternative hypotheses. We extend this result for residuals from functional linear models and develop a bootstrap diagnostic test for the presence of heteroscedasticity under the postulated model. Moreover, our approach also allows testing for "relevant" deviations from the homoscedastic variance structure and constructing confidence intervals for the proposed measure. We investigate the performance of our method using extensive numerical simulations and a data example.

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