*Tid:***29 oktober 2007 kl 15.15-17.00 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Martin Ohlson, Matematiska institutionen, Linköpings universitet och
tekniska högskola**

* Titel: *
The likelihood ratio statistic for testing spatial independence
using a separable covariance matrix

* Sammanfattning: *
Spatio-temporal processes like multivariate time series and
stochastic processes occur in many applications, for example the
observations from functional magnetic resonance imaging (fMRI)
or positron emission tomography (PET). It is interesting to test
independence between k sets of the variables, that is testing spatial
independence.

This talk deals with the problem of testing spatial independence for dependent observations. The sample observation matrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. The main results in this talk are the computations of the maximum likelihood estimators and the null distribution of the likelihood ratio statistic. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimators are computed and the asymptotic null distribution is shown to be similar to the independent observation case. In the case when the temporal covariance is unknown, the maximum likelihood estimators of the parameters are found by an iterative alternating algorithm.