Goodness of fit test for ergodic diffusion processes

Ilia Negri; Yoichi Nishiyama

doi:10.1007/s10463-007-0162-0

Goodness of fit test for ergodic diffusion processes

Ilia Negri^*, Yoichi Nishiyama

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.

Original language	English
Pages (from-to)	919-928
Number of pages	10
Journal	Annals of the Institute of Statistical Mathematics
Volume	61
Issue number	4
DOIs	https://doi.org/10.1007/s10463-007-0162-0
Publication status	Published - 2009 Dec
Externally published	Yes

Keywords

Asymptotically distribution free tests
Consistent test
Empirical process

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s10463-007-0162-0

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abstract = "A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.",

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author = "Ilia Negri and Yoichi Nishiyama",

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AU - Negri, Ilia

AU - Nishiyama, Yoichi

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PY - 2009/12

Y1 - 2009/12

N2 - A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.

AB - A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.

KW - Asymptotically distribution free tests

KW - Consistent test

KW - Empirical process

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

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Goodness of fit test for ergodic diffusion processes

Abstract

Keywords

ASJC Scopus subject areas

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