Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-23T05:09:35.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results concerning symmetric distributions

Published online by Cambridge University Press:  17 April 2009

Sándor Csörgoö  and
C.R. Heathcote
Sándor Csörgoö
Affiliation:
József Attila Tudományegyetem, Bolyai Intézet, 6720 Szeged, Aradi vértamik tere 1, Hungary
C.R. Heathcote
Affiliation:
Department of Statistics, The Faculties, Australian National University, PO Box 4, Canberra, ACT 2600, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this note is to establish results of a technical nature concerning a stochastic process that appears to be useful in the study of certain problems in statistical inference. These problems concern a test for symmetry, a method for obtaining an adaptive estimator of the centre of symmetry, and the detection of outliers with respect to the normal distribution. Details of the applications will be presented elsewhere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 3 , June 1982 , pp. 327 - 335
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Chambers, R.L. and Heathcote, C.R., “On the estimation of slope and the identification of outliers in linear regression”, Biometrika 68 (1981), 21–33.CrossRefGoogle Scholar
[2]Csörgő, Sándor, “Limit behaviour of the empirical characteristic function”, Ann. Probab. 9 (1981), 130–144.CrossRefGoogle Scholar
[3]Csörgő, Sándor “Multivariate empirical characteristic functions”, z. Wahrsch. Verw. Gebiete 55 (1981), 203–229.CrossRefGoogle Scholar
[4]Csörgő, Sándor, “The theory of functional least squares”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar
[5]Feuerverger, Andrey and Mureika, Roman A., “The empirical characteristic function and its applications”, Ann. Statist. 5 (1977), 88–97.CrossRefGoogle Scholar
[6]Heathcote, C.R., “Linear regression by functional least squares”, Essays in Statistical Science. J. Appl. Probab. (to appear).Google Scholar
[7]Marcus, Michael B., “Weak convergence of the empirical characteristic function”, Ann. Probab. 9 (1981), 194–201.CrossRefGoogle Scholar