On ADF goodness-of-fit tests for perturbed dynamical systems

We consider the problem of construction of goodness-of-fit tests for diffusion processes with a small noise. The basic hypothesis is composite parametric and our goal is to obtain asymptotically distribution-free tests. We propose two solutions. The first one is based on a change of time, and the se...

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Veröffentlicht in:	Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2015-11, Vol.21 (4), p.2430-2456
1. Verfasser:	KUTOYANTS, YURY A.
Format:	Artikel
Sprache:	eng
Schlagworte:	asymptotically distribution free test Cramér–von Mises tests diffusion processes goodness of fit test perturbed dynamical systems
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Zusammenfassung:	We consider the problem of construction of goodness-of-fit tests for diffusion processes with a small noise. The basic hypothesis is composite parametric and our goal is to obtain asymptotically distribution-free tests. We propose two solutions. The first one is based on a change of time, and the second test is obtained using a linear transformation of the "naturar" statistics.
ISSN:	1350-7265 1573-9759
DOI:	10.3150/14-BEJ650