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ON THE GOODNESS OF FIT TEST FOR DISCRETELY OBSERVED SAMPLE FROM DIFFUSION PROCESSES: DIVERGENCE MEASURE APPROACH

이상열
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회지 (Journal of the KMS)|제47권 제6호|pp. 1137-1146

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참고문헌

키워드

diffusion processdiscretely observed samplegoodness of fit testweak convergence to a Brownian bridgeresidual empirical processphi-divergence test
주제분류수학

초록

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.

Abstract

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.

참고문헌 (20)

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  14. 이상열, "Residual empirical process for diffusion processes", 대한수학회지, 45(3), pp.683~693 (2008), 대한수학회
  15. S. Lee, "On residual empirical processes of stochastic regression models with applications to time series", Ann. Statist., 27(1), pp.237~261 (1999)
  16. L. Pardo, "Statistical Inference Based on Divergence Measures", pp.2006, Chapman & Hall
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  20. A. N. Shiryayev, "Essentials of Stochastic Finance" (1999), World Scientific Publishing Co., Inc.

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