Goodness of fit test for small diffusions by discrete time observations

Ilia Negri; Yoichi Nishiyama

doi:10.1007/s10463-009-0228-2

Goodness of fit test for small diffusions by discrete time observations

Ilia Negri, Yoichi Nishiyama^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on 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 alternative.

Original language	English
Pages (from-to)	211-225
Number of pages	15
Journal	Annals of the Institute of Statistical Mathematics
Volume	63
Issue number	2
DOIs	https://doi.org/10.1007/s10463-009-0228-2
Publication status	Published - 2011 Apr
Externally published	Yes

Keywords

Asymptotically distribution free test
Discrete time observations
Small diffusion process

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s10463-009-0228-2

Cite this

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title = "Goodness of fit test for small diffusions by discrete time observations",

abstract = "We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on 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 alternative.",

keywords = "Asymptotically distribution free test, Discrete time observations, Small diffusion process",

author = "Ilia Negri and Yoichi Nishiyama",

note = "Funding Information: Acknowledgments Part of this work was performed during the first author{\textquoteright}s visit to Tokyo in December 2007 and the second author{\textquoteright}s visit to Bergamo in May 2008 supported by MIUR 2006 Grant, and the kind hospitality of the Institute of Statistical Mathematics and the University of Bergamo is greatly appreciated. The authors thank Prof. Hiroki Masuda for helpful discussion, and the anonymous referee for constructive comments, especially for the suggestion on the estimator for ΣS0,σ as we stated in Sect. 5.",

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doi = "10.1007/s10463-009-0228-2",

language = "English",

volume = "63",

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TY - JOUR

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

AU - Negri, Ilia

AU - Nishiyama, Yoichi

N1 - Funding Information: Acknowledgments Part of this work was performed during the first author’s visit to Tokyo in December 2007 and the second author’s visit to Bergamo in May 2008 supported by MIUR 2006 Grant, and the kind hospitality of the Institute of Statistical Mathematics and the University of Bergamo is greatly appreciated. The authors thank Prof. Hiroki Masuda for helpful discussion, and the anonymous referee for constructive comments, especially for the suggestion on the estimator for ΣS0,σ as we stated in Sect. 5.

PY - 2011/4

Y1 - 2011/4

N2 - We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on 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 alternative.

AB - We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on 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 alternative.

KW - Asymptotically distribution free test

KW - Discrete time observations

KW - Small diffusion process

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DO - 10.1007/s10463-009-0228-2

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 2

ER -

Goodness of fit test for small diffusions by discrete time observations

Abstract

Keywords

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