TY  - JOUR
A1  - Ditzhaus, Marc
A1  - Gaigall, Daniel
T1  - A consistent goodness-of-fit test for huge dimensional and functional data
JF  - Journal of Nonparametric Statistics
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.
KW  - Cramér-von-Mises statistic
KW  - separable Hilbert space
KW  - huge dimensional data
KW  - functional data
Y1  - 2018
U6  - https://doi.org/10.1080/10485252.2018.1486402
SN  - 1029-0311
VL  - 30
IS  - 4
SP  - 834
EP  - 859
PB  - Taylor & Francis
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - On Hotelling’s T² test in a special paired sample case
JF  - Communications in Statistics - Theory and Methods
N2  - In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.
KW  - complete block symmetry
KW  - Hotelling’s T² test
KW  - likelihood ratio test
KW  - uniformly most powerful invariant test
Y1  - 2017
U6  - https://doi.org/10.1080/03610926.2017.1408828
SN  - 1532-415X
VL  - 48
IS  - 2
SP  - 257
EP  - 267
PB  - Taylor & Francis
CY  - London
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - Hotelling’s T² tests in paired and independent survey samples: An efficiency comparison
JF  - Journal of Multivariate Analysis
N2  - Hotelling’s T² tests in paired and independent survey samples are compared using the traditional asymptotic efficiency concepts of Hodges–Lehmann, Bahadur and Pitman, as well as through criteria based on the volumes of corresponding confidence regions. Conditions characterizing the superiority of a procedure are given in terms of population canonical correlation type coefficients. Statistical tests for checking these conditions are developed. Test statistics based on the eigenvalues of a symmetrized sample cross-covariance matrix are suggested, as well as test statistics based on sample canonical correlation type coefficients.
Y1  - 2017
U6  - https://doi.org/10.1016/j.jmva.2016.11.004
SN  - 0047-259X
VL  - 2017
IS  - 154
SP  - 177
EP  - 198
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - On an independence test approach to the goodness-of-fit problem
JF  - Journal of Multivariate Analysis
N2  - Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.
KW  - Goodness-of-fit test
KW  - Independence test
KW  - Parametric bootstrap
KW  - Vapnik–Čhervonenkis class
KW  - Gamma distribution
Y1  - 2015
U6  - https://doi.org/10.1016/j.jmva.2015.05.013
SN  - 0047-259X
VL  - 2015
IS  - 140
SP  - 193
EP  - 208
PB  - Elsevier
CY  - Amsterdam
ER  -