On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes

Kleptsyna, Marina; Kutoyants, Yury A.

doi:10.1007/s11203-014-9096-3

Cited by 8 publications

(14 citation statements)

References 14 publications

(22 reference statements)

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“…Our objective is to realize this program. A similar result for ergodic diffusion processes is contained in Kutoyants [12] (simple basic hypothesis) and Kleptsyna and Kutoyants [7] (parametric basic hypothesis).…”

Section: Introductionsupporting

confidence: 67%

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

Kutoyants¹

2015

Bernoulli

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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 "natural" statistics. This is an electronic reprint of the original article published by the ISI/BS in Bernoulli, 2015, Vol. 21, No. 4, 2430-2456. This reprint differs from the original in pagination and typographic detail.Our goal is to find goodness-of-fit (GoF) tests which are asymptotically distribution free (ADF), that is, we look for a test statistics whose limit distributions under null hypothesis do not depend on the underlying model given by the functions S(ϑ, t, x), σ(t, x) and the parameter ϑ. This work is a continuation of the study Kutoyants [9], where an ADF test was proposed in the case of simple basic hypothesis.The behaviour of stochastic systems governed by such equations (called perturbed dynamical systems) is well studied, see, for example, Freidlin and Wentzell [3] and the references therein. Estimation theory (parametric and non-parametric) for such models of observations is also well developped, see, for example, Kutoyants [8] and Yoshida [17,18].Let us remind the well-known basic results in this problem for the i.i.d. model. We start with the simple hypothesis. Suppose that we observe n i.i.d. r.v.'s (X 1 , .

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Section: Introductionsupporting

confidence: 67%

“…Observe that there are many publications dealing with this transformation (see, e.g., the paper Maglaperidze et al [15] and the references therein). Another direct proof is given in Kleptsyna and Kutoyants [7].…”

Section: Second Testmentioning

confidence: 90%

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

Kutoyants¹

2015

Bernoulli

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“…ϑ and then to use the consistent estimatorθ n for the threshold c ε θ n , Λ 0 . Another possibility is to use the linear transformation of the statisticū n (·), which transforms it in the Wiener process (see, e.g., [10] or [11]). In this work we follow the third approach: we show that the limit distribution of the statistic does not depend on ϑ 0 .…”

Section: Statement Of the Problem And Auxiliary Resultsmentioning

confidence: 99%