Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401On convergence of sample and population Hilbertian functional principal components467475943ENA. R.SoltaniDepartment of Statistics, Shiraz University and Department of Statistics and Operations Research, Kuwait
University, State of Kuwait.A. R.NematollahiDepartment of Statistics, Shiraz University, Shiraz, Iran.R.NasirzadehDepartment of Statistics, Shiraz University, Shiraz, Iran.Journal Article20150704In 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 and<br />population 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.http://bims.iranjournals.ir/article_943_8b2fe9fd106048633e7c8a769df8b090.pdf