Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T08:11:50.489Z Has data issue: false hasContentIssue false
  • English
  • Français

On the first zero of an empirical characteristic function

Published online by Cambridge University Press:  14 July 2016

H. U. Bräker  and
J. Hüsler
H. U. Bräker
Affiliation:
University of Bern
J. Hüsler*
Affiliation:
University of Bern
*
∗ Postal address: Department of Mathematical Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
Get access Rights & Permissions [Opens in a new window]

Abstract

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

Keywords

GAUSSIAN PROCESSESSTABLE LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 593 - 601
Copyright
Copyright © Applied Probability Trust 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Csorgo, S. (1981) Limit behaviour of the empirical characteristic function. Ann. Prob. 9, 130–144.CrossRefGoogle Scholar
Csorgo, S. and Heathcote, C. R. (1987) Testing for symmetry. Biometrika 74, 177–184.Google Scholar
Cuzick, J. (1981) Boundary crossing probabilities for stationary Gaussian processes and Brownian motion. Trans. Amer. Math. Soc. 263, 469–492.Google Scholar
Heathcote, C. R. and Hüsler, J. (1990) Estimating the first zero of an empirical characteristic function. Stoch. Proc. Appl. 35, 347–360.Google Scholar
Heathcote, C. R. and Welsh, A. H. (1983) The robust estimation of autoregressive processes by functional least squares. J. Appl. Prob. 20, 737–753.Google Scholar
Hüsler, J. (1989) First zeros of empirical characteristic functions and extreme values of Gaussian processes. In Statistical Data Analysis and Inference, ed, Dodge, Y., North Holland, Amsterdam, pp. 177–182.Google Scholar
Hüsler, J. (1990) Extreme values and high boundary crossings for locally stationary Gaussian processes. Ann. Prob. 18, 1141–1158.Google Scholar
Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.Google Scholar
Marcus, M. B. (1970) A bound for the distribution of the maximum of continuous Gaussian processes. Ann. Math. Statist. 41, 305–309.Google Scholar
Welsh, A. H. (1984) A note on scale estimates based on the empirical characteristic function and their application to test for normality. Statist. Prob. Lett. 2, 345–348.Google Scholar
Welsh, A. H. and Nicholls, D. F. (1986) Robust estimation of regression models with dependent regressors: the functional least squares approach. Economet. Theory 2, 132–150.CrossRefGoogle Scholar