Goodness-of-fit test for switching diffusion |
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Authors: | A Gassem |
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Institution: | 1.Laboratoire de Statistique et Processus,Université du Maine,Le Mans Cedex 9,France |
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Abstract: | We consider two Cramér–von Mises goodness-of-fit tests for hypotheses that the observed diffusion process has sign-type trend
coefficient based on empirical distribution function and empirical density function. It is shown that the limit distributions
of the proposed tests statistics are defined by the integral type functionals of continuous Gaussian processes. We study the
behavior of these statistics under the alternative hypothesis and we prove that the tests are consistent. We provide the Karhunen-Loève
expansion on
\mathbbR{\mathbb{R}} of the corresponding limiting processes and we show that the eigenfunctions in these expansions have expressions in term
of Bessel functions. |
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Keywords: | |
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