Perturbation of functional tensors with applications to covariance operators

✍ Scribed by Yves Romain

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 131 KB
• Volume: 58
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(02)00104-9

✦ Synopsis

In this paper, results on the perturbation theory of symmetric operators are given. They concern the tensor extension of a perturbation problem for operators as studied by Fine (Statistics 18 (1987) 401). We consider functional deÿnitions of the tensor product, sum and di erence of operators and we study the eigenelement expansions of their perturbations. We show that the main result may be summarized in a simple form called "a perturbation rule for tensor operators". Finally, we indicate brie y how to apply these properties in a multivariate statistical sampling framework.