Details
| Original language | English |
|---|---|
| Pages (from-to) | 1396 - 1436 |
| Number of pages | 41 |
| Journal | Statistics |
| Volume | 53 |
| Issue number | 6 |
| Publication status | Published - 5 Nov 2019 |
Abstract
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.
Keywords
- Volume of confidence regions, asymptotic relative efficiency, likelihood ratio test, multinomial distribution, multivariate normal distribution
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Statistics, Vol. 53, No. 6, 05.11.2019, p. 1396 - 1436.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - On an asymptotic relative efficiency concept based on expected volumes of confidence regions
AU - Gaigall, Daniel
AU - Baringhaus, Ludwig
N1 - Publisher Copyright: © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/11/5
Y1 - 2019/11/5
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.
AB - 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 - multinomial distribution
KW - multivariate normal distribution
UR - http://www.scopus.com/inward/record.url?scp=85075606539&partnerID=8YFLogxK
U2 - 10.1080/02331888.2019.1683560
DO - 10.1080/02331888.2019.1683560
M3 - Article
VL - 53
SP - 1396
EP - 1436
JO - Statistics
JF - Statistics
SN - 0323-3944
IS - 6
ER -