• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

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.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.179-183
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• 2010

In this paper, we consider the change point problem in diusion processes based on discretely observed sample. Particularly, we consider the change point test for the dispersion parameter when the drift has unknown parameters. In performing a test, we employ the cusum of squares test based on the residuals. It is shown that the test has a limiting distribution of the sup of a Brownian bridge. A simulation result as to the Ornstein-Uhlenbeck process is provided for illustration. It demonstrates the validity of our test.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.839-845
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• 2011

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.547-554
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• 2010

In this paper, we extend the work by Lee et al. (2010) to multidimensional di usion processes. A test statistic analogous to the one-dimensional case is proposed to inves-tigate the joint stability of covariance matrix parameters and, under certain regularity conditions, is shown to have a limiting distribution of the sup of a multidimensional Brownian bridge. A simulation result is provided for illustration.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.267-280
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• 2007

In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.