A change detection procedure for an ergodic diffusion process

Tsukuda, Koji

doi:10.1007/s10463-016-0564-y

Cited by 5 publications

(2 citation statements)

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“…In the cases where a continuous observation is assumed to be obtained, detection of drift parameter change is typically considered because dispersion coefficient can be exactly estimated in this framework. See, for example, Negri and Nishiyama (2012) and Tsukuda (2017).…”

Section: Introductionmentioning

confidence: 99%

Robust test for dispersion parameter change in discretely observed diffusion processes

Song

2020

Computational Statistics & Data Analysis

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This paper deals with the problem of testing for dispersion parameter change in discretely observed diffusion processes when the observations are contaminated by outliers. To lessen the impact of outliers, we first calculate residuals using a robust estimate and then propose a trimmed-residual based CUSUM test. The proposed test is shown to converge weakly to a function of the Brownian bridge under the null hypothesis of no parameter change. We conduct simulations to evaluate performances of the proposed test in the presence of outliers. Numerical results confirm that the proposed test posses a strong robust property against outliers. In real data analysis, we fit the Ornstein-Uhlenbeck process to KOSPI200 volatility index data and locate some change points that are not detected by a naive CUSUM test.

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Section: Introductionmentioning

confidence: 99%

Robust test for dispersion parameter change in discretely observed diffusion processes

Song

2020

Computational Statistics & Data Analysis

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“…log n} − u u(1 − u)θ log n dN 1 (t) 0<u<1 = θ log n 0 1{t ≤ uθ log n} − u u(1 − u)θ log n (dN 1 (t) − dt) 0<u<1Theorem 4 ofTsukuda (2016) yields that (P • 5 (u)) 0<u<1 ⇒ (B • (u)/ √ u) 0<u<1 by setting H s = 1 with d = 1,λ s = 1 and T = θ log n. Consequently, we have (6.10). This completes the proof.A Appendix.…”

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confidence: 99%

On Poisson approximations for the Ewens sampling formula when the mutation parameter grows with the sample size

Tsukuda

2019

Ann. Appl. Probab.

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The Ewens sampling formula was firstly introduced in the context of population genetics by Warren John Ewens in 1972, and has appeared in a lot of other scientific fields. There are abundant approximation results associated with the Ewens sampling formula especially when one of the parameters, the sample size n or the mutation parameter θ which denotes the scaled mutation rate, tends to infinity while the other is fixed. By contrast, the case that θ grows with n has been considered in a relatively small number of works, although this asymptotic setup is also natural. In this paper, when θ grows with n, we advance the study concerning the asymptotic properties of the total number of alleles and of the counts of components in the allelic partition assuming the Ewens sampling formula, from the viewpoint of Poisson approximations.

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Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations

Tonaki

Kaino

Uchida

2021

Stat Inference Stoch Process

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A change detection procedure for an ergodic diffusion process

Cited by 5 publications

References 20 publications

Robust test for dispersion parameter change in discretely observed diffusion processes

Robust test for dispersion parameter change in discretely observed diffusion processes

On Poisson approximations for the Ewens sampling formula when the mutation parameter grows with the sample size

Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations

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