In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. The estimation of parameters using a flip-flop algorithm is also briefly discussed.
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. The test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly… (More)
Objective To determine if immediate (within 6 hours of adequate resuscitation) single-stage repair of complex craniofacial injuries could be accomplished with acceptable morbidity and mortality taking into consideration the cosmetic appearance of the patient. Patients and Methods A total of 26 patients (19 men, 7 women) ranging in age from 8 to 58 years… (More)
Some recent papers consider estimation of a covariance matrix with Kronecker structure of higher order. Singull et al. (2012) and Manceur and Dutilleul (2013) extend the estimation procedure for the matrix normal distribution to the multilinear normal distribution of order three and Ohlson et al. (2013) consider the case of higher order tensors of order k.… (More)
A note on mean testing for high dimensional multivariate data under non-normality, 2013, Statistica neerlandica (Print), (67), 1, 81-99. Abstract A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not… (More)