Goodness-of-fit test for ergodic diffusions by discrete-time observations: An innovation martingale approach

Hiroki Masuda; Ilia Negri; Yoichi Nishiyama

doi:10.1080/10485252.2010.510186

Goodness-of-fit test for ergodic diffusions by discrete-time observations: An innovation martingale approach

Hiroki Masuda, Ilia Negri, Yoichi Nishiyama^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure.We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free.We also show that our test is consistent under any fixed alternatives.

Original language	English
Pages (from-to)	237-254
Number of pages	18
Journal	Journal of Nonparametric Statistics
Volume	23
Issue number	2
DOIs	https://doi.org/10.1080/10485252.2010.510186
Publication status	Published - 2011 Jun
Externally published	Yes

Keywords

Asymptotically distribution-free test
Discrete-time observation
Ergodic diffusion process
Invariance principle

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/10485252.2010.510186

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title = "Goodness-of-fit test for ergodic diffusions by discrete-time observations: An innovation martingale approach",

abstract = "We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure.We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free.We also show that our test is consistent under any fixed alternatives.",

keywords = "Asymptotically distribution-free test, Discrete-time observation, Ergodic diffusion process, Invariance principle",

author = "Hiroki Masuda and Ilia Negri and Yoichi Nishiyama",

note = "Funding Information: This work was supported by MIUR 2006 Grant and ISM Cooperative Research Program.",

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doi = "10.1080/10485252.2010.510186",

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T1 - Goodness-of-fit test for ergodic diffusions by discrete-time observations

T2 - An innovation martingale approach

AU - Masuda, Hiroki

AU - Negri, Ilia

AU - Nishiyama, Yoichi

N1 - Funding Information: This work was supported by MIUR 2006 Grant and ISM Cooperative Research Program.

PY - 2011/6

Y1 - 2011/6

N2 - We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure.We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free.We also show that our test is consistent under any fixed alternatives.

AB - We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure.We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free.We also show that our test is consistent under any fixed alternatives.

KW - Asymptotically distribution-free test

KW - Discrete-time observation

KW - Ergodic diffusion process

KW - Invariance principle

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ER -

Goodness-of-fit test for ergodic diffusions by discrete-time observations: An innovation martingale approach

Abstract

Keywords

ASJC Scopus subject areas

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