Tests for high-dimensional covariance matrices using the theory of U-statistics

Sammanfattning

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

Nyckelord

covariance testing; U-statistics; high-dimensional data; sphericity

Publicerad i

Journal of Statistical Computation and Simulation
2015, volym: 85, nummer: 13, sidor: 2619-2631
Utgivare: TAYLOR & FRANCIS LTD

SLU författare

• Ahmad, Rauf

  • Institutionen för energi och teknik, Sveriges lantbruksuniversitet
    
  • Uppsala universitet

• von Rosen, Dietrich

  • Institutionen för energi och teknik, Sveriges lantbruksuniversitet
    
  • Linköpings universitet

UKÄ forskningsämne

Beräkningsmatematik

Publikationens identifierare

• DOI: https://doi.org/10.1080/00949655.2014.948441

Permanent länk till denna sida (URI)

https://res.slu.se/id/publ/75523