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  - 
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  -