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  - http://dx.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
A1  - Thiele, Jan Philipp
T1  - Statistical inference for L²-distances to uniformity
JF  - Computational Statistics
N2  - The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for L²-distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the L²-distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.
KW  - Integrated empirical distribution (survival) function
KW  - Goodness-of-fit tests for uniformity
KW  - Numerical inversion of Laplace transforms
KW  - Coverage probability
KW  - Equivalence test
Y1  - 2018
U6  - http://dx.doi.org/10.1007/s00180-018-0820-0
SN  - 1613-9658
VL  - 2018
IS  - 33
SP  - 1863
EP  - 1896
PB  - Springer
CY  - Berlin
ER  -