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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2010; 47(6): 1137-1146

Printed November 1, 2010

https://doi.org/10.4134/JKMS.2010.47.6.1137

Copyright © The Korean Mathematical Society.

On the goodness of fit test for discretely observed sample from diffusion processes: divergence measure approach

Sangyeol Lee

Seoul National University

Abstract

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In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

Keywords: diffusion process, discretely observed sample, residual empirical process, weak convergence to a Brownian bridge, goodness of fit test, phi-divergence test

MSC numbers: 60J60, 62F05

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