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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This work has been partially supported by the local grant sponsored by University of Bergamo: Theoretical and computational problems in statistics for continuously and discretely observed diffusion processes and by MIUR 2004 Grant
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Negri, I., Nishiyama, Y. Goodness of fit test for ergodic diffusion processes. Ann Inst Stat Math 61, 919–928 (2009). https://doi.org/10.1007/s10463-007-0162-0
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DOI: https://doi.org/10.1007/s10463-007-0162-0