Fourier approach to goodness-of-fit tests for Gaussian random processes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10472389" target="_blank" >RIV/00216208:11320/24:10472389 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wH7uYUC.kx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wH7uYUC.kx</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00362-023-01510-4" target="_blank" >10.1007/s00362-023-01510-4</a>
Alternative languages
Result language
angličtina
Original language name
Fourier approach to goodness-of-fit tests for Gaussian random processes
Original language description
A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the Cramer-von Mises distance between the observed empirical characteristic functional (CF) and the theoretical CF corresponding to the null hypothesis stating that the functional observations (process paths) were generated from a specific parametric family of Gaussian processes, possibly with unknown parameters. The asymptotic null distribution of the proposed test statistic is derived also in the presence of these nuisance parameters, the consistency of the classical parametric bootstrap is established, and some particular choices of the necessary tuning parameters are discussed. The empirical level and power are investigated in a simulation study involving GoF tests of an Ornstein-Uhlenbeck process, Vasi & ccaron;ek model, or a (fractional) Brownian motion, both with and without nuisance parameters, with suitable Gaussian and non-Gaussian alternatives.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Statistical Papers
ISSN
0932-5026
e-ISSN
1613-9798
Volume of the periodical
65
Issue of the periodical within the volume
5
Country of publishing house
DE - GERMANY
Number of pages
36
Pages from-to
2937-2972
UT code for WoS article
001111969600001
EID of the result in the Scopus database
2-s2.0-85178450396