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Aspects of multilinear algebra in statistical analysis of seasonal multivariate time series

Holmquist, Björn LU (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 well-known 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 well-known 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 non-central 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:
author
supervisor
opponent
  • Professor Eaton, Morris L, University of Minnesota, Minneapolis
organization
publishing date
type
Thesis
publication status
published
subject
pages
219 pages
publisher
Department of Mathematical Statistics, Lund University
defense location
MH:C
defense date
1985-06-07 10:00
language
English
LU publication?
yes
id
6ee82bd9-5239-4d03-a6bc-7fdcb4c83cad (old id 4934129)
date added to LUP
2016-03-18 12:20:50
date last changed
2016-09-19 08:45:06
@misc{6ee82bd9-5239-4d03-a6bc-7fdcb4c83cad,
  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 well-known 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 non-central 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},
  pages        = {219},
  publisher    = {ARRAY(0x9dd0d90)},
  title        = {Aspects of multilinear algebra in statistical analysis of seasonal multivariate time series},
  year         = {1985},
}