Weak convergence for the covariance operators of a Hilbertian linear process

André Mas

Stochastic Processes and their Applications, 2002, vol. 99, issue 1, 117-135

Abstract: Let Xt=[summation operator]k=-[infinity]+[infinity]ak([var epsilon]t-k) be a linear process with values in a Hilbert space H. The H valued r.v. [var epsilon]k are i.i.d. centered, the ak's are linear operators. We prove a central limit theorem for the vector of empirical covariance operators of the random variables Xt at orders 0 to in the space of Hilbert-Schmidt operators. Statistical applications are given in the area of principal component analysis for vector dependent random curves.

Keywords: Linear; operators; on; Hilbert; space; Covariance; operators; Weak; convergence; of; random; elements (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (19)

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