Goodness-of-fit test for switching diffusion

Gassem, Anis

doi:10.1007/s11203-010-9040-0

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…and the corresponding tests ψ T = 1 {δ T >cα} and φ T = 1 {γ T >dα} . Then using this weak convergence we can define the constants c α , d α (see [12], section 5.4 and Gassem [6]). We can consider the similar problem in the asymptotics of small noise, i.e., to use the limit behavior of the local time in the construction of the GoF tests.…”

Section: On Local Time and Gof Testingmentioning

confidence: 99%

Goodness-of-fit tests for perturbed dynamical systems

Kutoyants

2011

Journal of Statistical Planning and Inference

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a b s t r a c tWe consider the goodness-of-fit testing problem for stochastic differential equation with small diffusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of the type of Cramé r-von Mises, Kolmogorov-Smirnov and Chi-Square. The power functions of these tests we study for a special classes of close alternatives. We discuss the construction of the goodness-of-fit test based on the local time.

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Section: On Local Time and Gof Testingmentioning

confidence: 99%

Goodness-of-fit tests for perturbed dynamical systems

Kutoyants

2011

Journal of Statistical Planning and Inference

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“…Therefore the corresponding tests ψ T and Ψ T are ADF. The limit distribution of the test statistic δ T with h (x) ≡ 1 were studied by Gassem [8], who obtained the Karhunen-Loeve expansion for the limit Gaussian process ζ (·).…”

Section: Examplesmentioning

confidence: 99%

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

Kutoyants

2010

Journal of Nonparametric Statistics

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We consider the goodness-of-fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We study the asymptotic distribution of the Cramér-von Mises type tests based on the empirical distribution function and local time estimator of the invariant density. Particularly, we propose a transformation which makes these tests asymptotically distribution-free.

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“…It is also known as the Principal Component Analysis (PCA) [13,11] and "is probably the oldest and best known of the techniques of multivariate analysis" [13]. This technique is intensively used in a vide range of research areas such as data compression [14,15], pattern recognition [16], interference suppression [17], image processing [18], forecasting [19], hydrology [20], physics nonlinear phenomena [21], probabilistic mechanics [22,23], biomechanics [24], geoscience [25,26], stochastic processes [27,28], information theory [29,30], 3-D object classification and video coding [31], chemical theory [32], oceanology [33], optics and laser technology [34] and others.…”

Section: Introductionmentioning

confidence: 99%

A new technique for compression of data sets

Torokhti¹

2021

Preprint

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Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this paper allows us to substantially improve all the four issues above.The proposed transform F is presented in the form of a sum with p−1 terms, F 1 , . . . , F p−1 , where each term is a particular sub-transform presented by a first degree polynomial. For j = 1, . . . , p−1, each sub-transform F j is determined from interpolation-like conditions. This device provides the transform flexibility to incorporate variation of observed data and leads to performance improvement. The transform F has two degrees of freedom, the number of sub-transforms and associated compression ratio associated with each sub-transform F j .

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Goodness-of-fit test for switching diffusion

Abstract: Goodness of fit tests, Cramér–von Mises tests, Karhunen-Loève expansion, Gaussian processes, Bessel functions, Asymptotic properties, Consistent tests, 62G10, 62G20, 62M02,

Cited by 6 publications

References 8 publications

Goodness-of-fit tests for perturbed dynamical systems

Goodness-of-fit tests for perturbed dynamical systems

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

A new technique for compression of data sets

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