Limit distributions of V- and U-statistics in terms of multiple stochastic Wiener-type integrals
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Contributors
Abstract
We describe the limit distribution of V- and U-statistics in a new fashion. In the case of V-statistics the limit variable is a multiple stochastic integral with respect to an abstract Brownian bridge GQ. This extends the pioneer work of Filippova (1961) [8]. In the case of U-statistics we obtain a linear combination of GQ-integrals with coefficients stemming from Hermite Polynomials. This is an alternative representation of the limit distribution as given by Dynkin and Mandelbaum (1983) [7] or Rubin and Vitale (1980) [13]. It is in total accordance with their results for product kernels.
Details
Original language | English |
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Pages (from-to) | 306-314 |
Number of pages | 9 |
Journal | Journal of Multivariate Analysis |
Volume | 102 |
Issue number | 2 |
Publication status | Published - Feb 2011 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- 60F05, 60H05, 62E20