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A weak convergence theorem for the empirical characteristic function

Published online by Cambridge University Press:  14 July 2016

John T. Kent
John T. Kent*
Affiliation:
University of Cambridge
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Abstract

The purpose of this paper is to show that the empirical characteristic function, when suitably normalised, converges weakly to a stationary Gaussian process whose autocovariance function is the theoretical characteristic function.

Keywords

WEAK CONVERGENCEEMPIRICAL CHARACTERISTIC FUNCTIONSTATIONARY GAUSSIAN PROCESSQUANTOGRAM
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 515 - 523
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[2] Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
[3] Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II. Wiley, New York.Google Scholar
[4] Kendall, D. G. (1974) Hunting quanta. Phil. Trans. Roy. Soc. London A 276, 231–266. See also the corrections and additions set out in the discussion following Mardia, K. V. Statistics of directional data. J. R. Statist. Soc. B (To appear.) Google Scholar