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Functional limit theory for the spectral covariance estimator

Part of: Limit theorems Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Dominique Dehay  and
Jacek Leśkow
Dominique Dehay*
Affiliation:
Université de Rennes 1
Jacek Leśkow*
Affiliation:
University of California, Santa Barbara
*
∗Postal address: IRMAR, Université de Rennes 1, Campus Beaulieu, 35042 Rennes, France.
∗∗Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106–3110, USA.
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Abstract

Processes that exhibit repeatability in their kth-order moments are frequently studied in signal analysis. Such repeatability can be conveniently expressed with the help of almost periodicity. In particular, almost periodically correlated (APC) processes play an important role in the analysis of repeatable signals. This paper presents a study of asymptotic distributions of the estimator of the spectral covariance function for APC processes. It is demonstrated that, for a large class of APC processes, the functional central limit theorem holds.

Keywords

ALMOST PERIODIC PROCESSFUNCTIONAL CENTRAL LIMIT THEOREMMIXING PROPERTY

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62G20: Asymptotic properties
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1077 - 1092
Copyright
Copyright © Applied Probability Trust 1996 

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