Aspects of multilinear algebra in statistical analysis of seasonal multivariate time series
(1985) Abstract
 Representations of concepts from multivariate statistics are studied using multilinear algebra. Applications are given to the analysis of seasonal multivariate time series.
The first paper concerns a class of permutation matrices which are representations of permutation operators on tensor spaces.
In the second paper, the derivation of moments and cumulants of Hilbert space valued random variables are studied. Relations between moments and cumulants  as vector space elements  are given which generalize wellknown results for scalar random variables. Representations of differentials are discussed and results for differentials of matrix valued functions with matrix arguments are derived. Moments and... (More)  Representations of concepts from multivariate statistics are studied using multilinear algebra. Applications are given to the analysis of seasonal multivariate time series.
The first paper concerns a class of permutation matrices which are representations of permutation operators on tensor spaces.
In the second paper, the derivation of moments and cumulants of Hilbert space valued random variables are studied. Relations between moments and cumulants  as vector space elements  are given which generalize wellknown results for scalar random variables. Representations of differentials are discussed and results for differentials of matrix valued functions with matrix arguments are derived. Moments and cumulants of the noncentral Wishart distribution are given.
in the third paper, seasonal multivariate time series are investigated using the concepts described in the first two papers. Estimators of unknown parameters are given and their asymptotic distributions are derived. Test statistics for testing homogeneity in time and independence of subprocesses are given and also their asymptotic distributions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4934129
 author
 Holmquist, Björn ^{LU}
 supervisor

 Gunnar Blom ^{LU}
 opponent

 Professor Eaton, Morris L, University of Minnesota, Minneapolis
 organization
 publishing date
 19850607
 type
 Thesis
 publication status
 published
 subject
 pages
 219 pages
 publisher
 Department of Mathematical Statistics, Lund University
 defense location
 MH:C
 defense date
 19850607 10:00:00
 language
 English
 LU publication?
 yes
 id
 6ee82bd952394d03a6bc7fdcb4c83cad (old id 4934129)
 date added to LUP
 20160404 10:43:18
 date last changed
 20200830 02:29:47
@phdthesis{6ee82bd952394d03a6bc7fdcb4c83cad, abstract = {{Representations of concepts from multivariate statistics are studied using multilinear algebra. Applications are given to the analysis of seasonal multivariate time series.<br/><br> <br/><br> The first paper concerns a class of permutation matrices which are representations of permutation operators on tensor spaces.<br/><br> <br/><br> In the second paper, the derivation of moments and cumulants of Hilbert space valued random variables are studied. Relations between moments and cumulants  as vector space elements  are given which generalize wellknown results for scalar random variables. Representations of differentials are discussed and results for differentials of matrix valued functions with matrix arguments are derived. Moments and cumulants of the noncentral Wishart distribution are given.<br/><br> <br/><br> in the third paper, seasonal multivariate time series are investigated using the concepts described in the first two papers. Estimators of unknown parameters are given and their asymptotic distributions are derived. Test statistics for testing homogeneity in time and independence of subprocesses are given and also their asymptotic distributions.}}, author = {{Holmquist, Björn}}, language = {{eng}}, month = {{06}}, publisher = {{Department of Mathematical Statistics, Lund University}}, school = {{Lund University}}, title = {{Aspects of multilinear algebra in statistical analysis of seasonal multivariate time series}}, year = {{1985}}, }