The asymptotic distribution of a cluster-index for i.i.d. normal random variables
Yannis G. Yatracos
Source: Ann. Appl. Probab. Volume 19, Number 2
(2009), 585-595.
Abstract
In a sample variance decomposition, with components functions of the sample’s spacings, the largest component Ĩn is used in cluster detection. It is shown for normal samples that the asymptotic distribution of Ĩn is the Gumbel distribution.
First Page:
Show
Hide
Primary Subjects:
60F05
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702242
Digital Object Identifier: doi:10.1214/08-AAP553
Zentralblatt MATH identifier: 05566092
Mathematical Reviews number (MathSciNet): MR2521880
References
Chow, Y. S. and Teicher, H. (1988). Probability Theory: Independence, Interchangeability, Martingales, 2nd ed. Springer, New York.
Mathematical Reviews (MathSciNet): MR953964
David, H. A. and Nagaraja, H. N. (2003). Order Statistics, 3rd ed. Wiley, Hoboken, NJ.
Mathematical Reviews (MathSciNet): MR1994955
Deheuvels, P. (1982). Strong limiting bounds for maximal uniform spacings. Ann. Probab. 10 1058–1065.
Mathematical Reviews (MathSciNet): MR672307
Zentralblatt MATH: 0505.60033
Digital Object Identifier: doi:10.1214/aop/1176993728
Project Euclid: euclid.aop/1176993728
Deheuvels, P. (1983). Upper bounds for kth maximal spacings. Z. Wahrsch. Verw. Gebiete 62 465–474.
Mathematical Reviews (MathSciNet): MR690571
Deheuvels, P. (1984). Strong limit theorems for maximal spacings from a general univariate distribution. Ann. Probab. 12 1181–1193.
Mathematical Reviews (MathSciNet): MR757775
Zentralblatt MATH: 0558.62018
Digital Object Identifier: doi:10.1214/aop/1176993147
Project Euclid: euclid.aop/1176993147
Deheuvels, P. (1985). The limiting behaviour of the maximal spacing generated by an i.i.d. sequence of Gaussian random variables. J. Appl. Probab. 22 816–827.
Mathematical Reviews (MathSciNet): MR808861
Zentralblatt MATH: 0584.60033
Digital Object Identifier: doi:10.2307/3213949
JSTOR: links.jstor.org
Devroye, L. (1981). Laws of the iterated logarithm for order statistics of uniform spacings. Ann. Probab. 9 860–867.
Mathematical Reviews (MathSciNet): MR628878
Zentralblatt MATH: 0465.60038
Digital Object Identifier: doi:10.1214/aop/1176994313
Project Euclid: euclid.aop/1176994313
Devroye, L. (1982). A log log law for maximal uniform spacings. Ann. Probab. 10 863–868.
Mathematical Reviews (MathSciNet): MR659558
Zentralblatt MATH: 0491.60030
Digital Object Identifier: doi:10.1214/aop/1176993799
Project Euclid: euclid.aop/1176993799
Devroye, L. (1984). The largest exponential spacing. Utilitas Math. 25 303–313.
Mathematical Reviews (MathSciNet): MR752867
Diaconis, P. and Freedman, D. (1984). Asymptotics of graphical projection pursuit. Ann. Statist. 12 793–815.
Mathematical Reviews (MathSciNet): MR751274
Zentralblatt MATH: 0559.62002
Digital Object Identifier: doi:10.1214/aos/1176346703
Project Euclid: euclid.aos/1176346703
Ibragimov, I. A. and Linnik, Y. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff Publishing, Groningen. With a supplementary chapter by I. A. Ibragimov and V. V. Petrov, Translation from the Russian edited by J. F. C. Kingman.
Mathematical Reviews (MathSciNet): MR322926
Zentralblatt MATH: 0219.60027
Nariaki, S. and Akihide, G. (1985). Pearson diagrams for truncated normal and truncated Weibull distributions. Biometrika 72 219–222.
Pyke, R. (1965). Spacings. (With discussion.) J. Roy. Statist. Soc. Ser. B 27 395–449.
Mathematical Reviews (MathSciNet): MR216622
JSTOR: links.jstor.org
Slud, E. (1977/78). Entropy and maximal spacings for random partitions. Z. Wahrsch. Verw. Gebiete 41 341–352.
Mathematical Reviews (MathSciNet): MR488242
Digital Object Identifier: doi:10.1007/BF00533604
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
Mathematical Reviews (MathSciNet): MR595165
Yatracos, Y. G. (1998). Variance and clustering. Proc. Amer. Math. Soc. 126 1177–1179.
Mathematical Reviews (MathSciNet): MR1458273
Zentralblatt MATH: 0896.62062
Digital Object Identifier: doi:10.1090/S0002-9939-98-04524-9
JSTOR: links.jstor.org
Yatracos, Y. G. (2007). Cluster identification via projection pursuit. Unpublished manuscript.
The Annals of Applied Probability
