Details
| Original language | English |
|---|---|
| Pages (from-to) | 834 - 859 |
| Number of pages | 26 |
| Journal | Journal of Nonparametric Statistics |
| Volume | 30 |
| Issue number | 4 |
| Early online date | 20 Jun 2018 |
| Publication status | Published - 2018 |
Abstract
A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
Keywords
- Cramér-von-Mises statistic, functional data, huge dimensional data, separable Hilbert space
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of Nonparametric Statistics, Vol. 30, No. 4, 2018, p. 834 - 859.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - A consistent goodness-of-fit test for huge dimensional and functional data
AU - Gaigall, Daniel
AU - Ditzhaus, Marc
N1 - Publisher Copyright: © 2018, © American Statistical Association and Taylor & Francis 2018.
PY - 2018
Y1 - 2018
N2 - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
AB - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
KW - Cramér-von-Mises statistic
KW - functional data
KW - huge dimensional data
KW - separable Hilbert space
UR - http://www.scopus.com/inward/record.url?scp=85048746873&partnerID=8YFLogxK
U2 - 10.1080/10485252.2018.1486402
DO - 10.1080/10485252.2018.1486402
M3 - Article
VL - 30
SP - 834
EP - 859
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
SN - 1048-5252
IS - 4
ER -