Locations of extreme values of the empirical process

• Autorzy: Randjiou Y.
• Języki publikacji: EN

Abstrakty

EN

Let α_n be a uniform empirical process and μ_n (respectively, ν_n the unique location of its maximum (respectively, minimum). We establish a “liminf” iterated logarithm law for |μ_n – ν_n|

Słowa kluczowe

EN

empirical process; iterated logarithm

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 1
• Strony: 57--70
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Randjiou Y.

• Laboratoire de Probabilités Université, Paris VI, 4 place jussieu, F-75252 Paris Cedex 05, France

Bibliografia

• [1] M. Csörgő and P. Révész, Strong Approximations in Probability und Statistics, Academic Press, New York 1981.
• [2] K. Itô and H. P. McKean, Diffusion Processes and Their Sample Paths, Springer, Berlin 1965.
• [3] J. Komlós, P. Major and G. Tusnády, An approximation of partial sums of independent R.V.’s and the sample DF. I, Z. Wahrscheinlichkeitstheorie verw. Gebiete 32 (1975), pp. 111-131.
• [4] Z. Shi, Locating the maximum of an empirical process, Statist. Probab. Lett. 31 (1995), pp. 199-211.
• [5] G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York 1986.