TY - JOUR
T1 - Resampling U-statistics using p-stable laws
AU - Dehling, Herold
AU - Denker, Manfred
AU - Woyczynski, Wojbor A.
N1 - Funding Information:
Received July 27, 1987; revised October 31, 1988. AMS 1980 subject classifications: 62699, 6OH05, 60F17. Key words and phrases: U-statistic, weak convergence, normal domain of attraction of the p-stable law, p-stable multiple stochastic integral. * This author thanks the faculty and staff of the Institut fiir Mathematische Stochastik of the University of Gottingen for their hospitality while this paper was being written. Partly supported by a grant from ONR.
PY - 1990/7
Y1 - 1990/7
N2 - It is well known that symmetric statistics based on a kernel with finite second moment have a limit law which can be described by a multiple Wiener-Ito integral. However, if the kernel has less than second moments, no weak limit law holds in general. In the present paper we show that by a suitable change of the empirical process this process has a p-stable multiple integral as its limit.
AB - It is well known that symmetric statistics based on a kernel with finite second moment have a limit law which can be described by a multiple Wiener-Ito integral. However, if the kernel has less than second moments, no weak limit law holds in general. In the present paper we show that by a suitable change of the empirical process this process has a p-stable multiple integral as its limit.
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U2 - 10.1016/0047-259X(90)90057-O
DO - 10.1016/0047-259X(90)90057-O
M3 - Article
AN - SCOPUS:38249020782
SN - 0047-259X
VL - 34
SP - 1
EP - 13
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 1
ER -