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
T1  - On an asymptotic relative efficiency concept based on expected volumes of confidence regions
JF  - Statistics - A Journal of Theoretical and Applied Statistic
N2  - The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.
KW  - Volume of confidence regions
KW  - asymptotic relative efficiency
KW  - likelihood ratio test
KW  - multivariate normal distribution
KW  - multinomial distribution
Y1  - 2019
U6  - http://dx.doi.org/10.1080/02331888.2019.1683560
SN  - 1029-4910
VL  - 53
IS  - 6
SP  - 1396
EP  - 1436
PB  - Taylor & Francis
CY  - London
ER  -