On L2 space approach to change point problems

Tsukuda, Koji; Nishiyama, Yoichi

doi:10.1016/j.jspi.2014.02.007

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…Using this norm instead of the supremum norm we get a Cramér‐von Mises‐type statistic. This

L^{2}

approach to change point analysis was also recently considered for independent observations by Tsudaka & Nishiyama ().…”

Section: Introductionmentioning

confidence: 99%

“…Using this norm instead of the supremums norm we get the statistic max 1≤m≤n−1 Ȳm − Ȳm+1;n , which is a Cramér-von Mises-type statistic. This L 2 approach to change-point analysis was also recently considered for independent observations by Tsudaka and Nishiyama [2014]. Critical values for change-point tests are often deduced from asymptotics.…”

Section: Introductionmentioning

confidence: 99%

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Sequential block bootstrap in a Hilbert space with application to change point analysis

2016

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A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a Hilbert space is required. The test can also be used to detect changes in the marginal distribution of random vectors, which is supplemented by a simulation study. Our methods are applied to hydrological data from Germany. The Canadian Journal of Statistics 44: 300–322; 2016 © 2016 Statistical Society of Canada

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“…Using this norm instead of the supremum norm we get a Cramér‐von Mises‐type statistic. This

L^{2}

approach to change point analysis was also recently considered for independent observations by Tsudaka & Nishiyama ().…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sequential block bootstrap in a Hilbert space with application to change point analysis

2016

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“…developed a functional analogue of the Kwiatkowski-Phillips-Schmidt-Shin test statistic for stationarity testing that does not rely on dimension reduction. Sharipov et al (2016) considered a bootstrap procedure for measuring the significance of the norms of functional cumulative sum processes with applications to testing for a structural break in the means of functional observations and in the distribution function of scalar time series observations under a mixing assumption, generalizing the result for the IID case that was put forward in Tsudaka and Nishiyama (2014). Bucchia and Wendler (2017) studied general bootstrap procedures for structural break analysis in Hilbert space-valued random fields.…”

Section: Introductionmentioning

confidence: 99%

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Aue

Rice

Sönmez

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

158

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Summary Methodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous estimators based on functional principal component analysis are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the procedures proposed.

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“…See also Tsukuda and Nishiyama (2014) who took an approach based on weak convergence in L 2 -spaces to this problem. Although Horváth and Parzen (1994) didn't discuss the asymptotic behavior of the test under the alternative, Negri and Nishiyama (2012) who took the same approach to the change point problem for an ergodic diffusion process model based on the continuous observation proved also the consistency of the test under an alternative which has sufficient generality.…”

Section: Introductionmentioning

confidence: 99%

Z-Process Method for Change Point Problems

Negri¹,

Nishiyama²

2021

Martingale Methods in Statistics

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The aim of this paper is to develop a general, unified approach, based on some partial estimation functions which we call "Z-process", to the change point problems. The method proposed can be applied not only to ergodic models but also to some models where the Fisher information matrix is random. Applications to some concrete models, including especially a parametric model for volatilities of diffusion processes are presented. Simulations for randomly time-transformed Brownian bridge process appearing as the limit of the proposed test statistics are performed with computer intensive use.

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On L2 space approach to change point problems

Cited by 5 publications

References 17 publications

Sequential block bootstrap in a Hilbert space with application to change point analysis

Sequential block bootstrap in a Hilbert space with application to change point analysis

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Z-Process Method for Change Point Problems

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