TY - JOUR
ID - 943
TI - On convergence of sample and population Hilbertian functional principal components
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Soltani, A. R.
AU - Nematollahi, A. R.
AU - Nasirzadeh, R.
AD - Department of Statistics, Shiraz University and Department of Statistics and Operations Research, Kuwait
University, State of Kuwait.
AD - Department of Statistics, Shiraz University, Shiraz, Iran.
Y1 - 2017
PY - 2017
VL - 43
IS - 2
SP - 467
EP - 475
KW - Hilbertian random elements
KW - functional data analysis
KW - functional principal component analysis
KW - covariance operators
KW - operator convergence.s
DO -
N2 - In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would imply the convergence of the corresponding sequences of the sample andpopulation eigenvalues and eigenvectors, and vice versa. In particular we prove that the principal component scores converge in distribution in certain family of Hilbertian elliptically contoured distributions.
UR - http://bims.iranjournals.ir/article_943.html
L1 - http://bims.iranjournals.ir/article_943_8b2fe9fd106048633e7c8a769df8b090.pdf
ER -