On the goodness-of-fit testing for ergodic diffusion processes

Kutoyants, Yury A.

doi:10.1080/10485250903359564

Cited by 10 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The goodness-of-fit test for diffusion processes based on continuous time observation, which is not studied in this paper, is considered in several works. See for example Dachian and Kutoyants (2008), Kutoyants (2010), Negri and Nishiyama (2009) and referenecs therein. Remark 1.6.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak convergences of marked empirical processes in a Hilbert space and their applications

Tsukuda,

Nishiyama

2018

Preprint

View full text Add to dashboard Cite

In this paper, weak convergences of marked empirical processes in L 2 (R, ν) and their applications to statistical goodness-of-fit tests are provided, where L 2 (R, ν) is the set of equivalence classes of the square integrable functions on R with respect to a finite Borel measure ν. The results obtained in our framework of weak convergences are, in the topological sense, weaker than those in the Skorokhod topology on a space of cádlág functions or the uniform topology on a space of bounded functions, which have been well studied in previous works. However, our results have the following merits: (1) avoiding conditions which do not suit for our purpose; (2) treating a weight function which makes us possible to propose an Anderson-Darling type test statistics for goodness-of-fit tests. Indeed, the applications presented in this paper are novel.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak convergences of marked empirical processes in a Hilbert space and their applications

Tsukuda,

Nishiyama

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…One way to have asymptotically distribution free statistic was proposed by Negri and Nishiyama [17]. Another possibility (discussed in [14]) is to use the weight functions. Let us illustrate the second approach on the statistic…”

Section: Proofsmentioning

confidence: 99%

“…where M(·) is some function providing the finitness of this integral and Ψ (ϑ 0 , x) = where W (·) is a Wiener process, i.e. ; we have asymptotically distribution free testψ T = 1I {Î 2 T (ϑ 0 )>rα} [14]. The threshold r α , of course, is solution of the following equation The similar result can be proved for the large class of functions M (·) satisfying the obvious conditions.…”

Section: Proofsmentioning

confidence: 99%

See 1 more Smart Citation

On identification of the threshold diffusion processes

Kutoyants

2010

Ann Inst Stat Math

Self Cite

View full text Add to dashboard Cite

We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series analysis threshold autoregressive (TAR) models. In such models the trend is switching when the observed process atteints some (unknown) values and the problem is to estimate it or to test some hypotheses concerning these values. The related statistical problems correspond to the singular estimation or testing, for example, the rate of convergence of estimators is T and not √ T as in regular estimation problems. We study the asymptotic behavior of the maximum likelihood and bayesian estimators and discuss the possibility of the construction of the goodness of fit test for such models of observation.

show abstract

“…However, due to the structure of the covariance of the limit process, the Kolmogorov-Smirnov statistics is not asymptotically distribution free in diffusion process models. More recently Kutoyants [10] has proposed a modification of the Kolmogorov-Smirnov statistics for diffusion models that became asymptotically distribution free. See also Dachian and Kutoyants [2] where they propose some GoF tests for diffusion and inhomogeneous Poisson processes with simple basic hypothesis.…”

Section: Introductionmentioning

confidence: 99%

On goodness-of-fit testing for ergodic diffusion process with shift parameter

Negri

Zhou

2014

Stat Inference Stoch Process

View full text Add to dashboard Cite

A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer-Von Mises type test statistics are studied. The first one is based on local time estimator of the invariant density, the second one is based on the empirical distribution function. The unknown parameter is estimated via the maximum likelihood estimator. It is shown that both the limit distributions of the two test statistics do not depend on the unknown parameter, so the distributions of the tests are asymptotically parameter free. Some considerations on the consistency of the proposed tests and some simulation studies are also given.

show abstract

On the goodness-of-fit testing for ergodic diffusion processes

Cited by 10 publications

References 16 publications

Weak convergences of marked empirical processes in a Hilbert space and their applications

Weak convergences of marked empirical processes in a Hilbert space and their applications

On identification of the threshold diffusion processes

On goodness-of-fit testing for ergodic diffusion process with shift parameter

Contact Info

Product

Resources

About