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On the quantogram of Kendall and Kent

Published online by Cambridge University Press:  14 July 2016

Sándor Csörgő
Sándor Csörgő*
Affiliation:
Szeged University
*
∗ Postal address: Bolyai Institute, Szeged University, H–6720 Szeged, Aradi vértanúk tere 1, Hungary.
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Abstract

The ‘snake' theorem, i.e., the weak convergence of the complex quantogram, is studied. The moment assumption is weakened by a strong approximation result of the author.

Keywords

QUANTOGRAMEMPIRICAL CHARACTERISTIC FUNCTIONWEAK CONVERGENCESTRONG APPROXIMATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 440 - 447
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research completed while the author was on leave from Szeged University and a Visiting Scientist at Carleton University, supported by Canadian N.R.C. operating grants of D. A. Dawson and J. N. K. Rao.

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Csörgő, S. (1980) Limit behaviour of the empirical characteristic function. Ann. Prob. 8.Google Scholar
Fernique, X. (1975) Régularité des trajectoires des fonctions gausiennes. École d'Été de Probabilités de Saint-Fleur IV, 1974. Lecture Notes in Mathematics 480, Springer-Verlag, Berlin, 1–96.Google Scholar
Kawata, T. (1972) Fourier Analysis in Probability Theory. Academic Press, New York.Google Scholar
Kendall, D. G. (1974) Hunting quanta. Phil. Trans. Roy. Soc. London A 276, 231–266. Second edition: (1977) Proc. Symp. In Honour of Jerzy Neyman, Warszawa, 1974, Polish Academy of Sciences, 111–159.Google Scholar
Kent, J. T. (1975) A weak convergence theorem for the empirical characteristic function. J. Appl. Prob. 12, 515–523.Google Scholar