Ahmad, Rauf
- Institutionen för energi och teknik, Sveriges lantbruksuniversitet
- Uppsala universitet
Sammanfattning
A two-sample test statistic is presented for testing the equality of mean vectors when the dimension, , exceeds the sample sizes, , and the distributions are not necessarily normal. Under mild assumptions on the traces of the covariance matrices, the statistic is shown to be asymptotically Chi-square distributed when . However, the validity of the test statistic when is fixed but large, including , and when the distributions are multivariate normal, is shown as special cases. This two-sample Chi-square approximation helps us establish the validity of Box's approximation for high-dimensional and non-normal data to a two-sample setup, valid even under Behrens-Fisher setting. The limiting Chi-square distribution of the statistic is obtained using the asymptotic theory of degenerate -statistics, and using a result from classical asymptotic theory, it is further extended to an approximate normal distribution. Both independent and paired-sample cases are considered.
Nyckelord
High-dimensional multivariate inference; Box's approximation; Behrens-Fisher setting; Degenerate U-statistics
Publicerad i
Annals of the Institute of Statistical Mathematics
2014, volym: 66, nummer: 1, sidor: 33-61
Utgivare: SPRINGER HEIDELBERG
SLU författare
UKÄ forskningsämne
Sannolikhetsteori och statistik
Publikationens identifierare
- DOI: https://doi.org/10.1007/s10463-013-0404-2
Permanent länk till denna sida (URI)
https://res.slu.se/id/publ/67644