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A sufficient condition for the CLT in the space of nuclear operators--Application to covariance of random functions

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  • Mas, André

Abstract

We give a sufficient condition for the CLT to hold in the space of trace class (nuclear) operators. This condition turns out to be adapted to the asymptotic study of empirical covariance operators of Hilbert valued random variables.

Suggested Citation

  • Mas, André, 2006. "A sufficient condition for the CLT in the space of nuclear operators--Application to covariance of random functions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1503-1509, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1503-1509
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    3. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
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