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Volumn 9, Issue 2, 1996, Pages 385-412

On integrability in the LIL for degenerate U-statistics

Author keywords

Completely degenerate (or canonical) U statistics; Law of the iterated logarithm

Indexed keywords


EID: 21344466941     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02214656     Document Type: Article
Times cited : (5)

References (13)
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    • (1993) J. Th. Prob. , vol.6 , pp. 101-122
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  • 2
    • 0000626858 scopus 로고
    • On the law of the iterated logarithm for canonical U-statistics and processes
    • Arcones, M., and Giné, E. (1994). On the law of the iterated logarithm for canonical U-statistics and processes. Stoch. Proc. Appl. 58, 217-245.
    • (1994) Stoch. Proc. Appl. , vol.58 , pp. 217-245
    • Arcones, M.1    Giné, E.2
  • 3
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    • Laws of large numbers for quadratic forms, maxima of products and truncated sums of i.i.d. random variables
    • Cuzick, J., Giné, E., and Zinn, J. (1995). Laws of large numbers for quadratic forms, maxima of products and truncated sums of i.i.d. random variables. Ann. Prob. 23, 292-333.
    • (1995) Ann. Prob. , vol.23 , pp. 292-333
    • Cuzick, J.1    Giné, E.2    Zinn, J.3
  • 4
    • 38249025450 scopus 로고
    • Complete convergence of triangular arrays and the law of the iterated logarithm for degenerate U-statistics
    • Dehling, H. (1989). Complete convergence of triangular arrays and the law of the iterated logarithm for degenerate U-statistics. Stat. Prob. Lett. 7, 319-321.
    • (1989) Stat. Prob. Lett. , vol.7 , pp. 319-321
    • Dehling, H.1
  • 5
    • 0000509434 scopus 로고
    • Decoupling and Khintchine inequalities for U-statistics
    • de la Peña, V. (1992). Decoupling and Khintchine inequalities for U-statistics. Ann. Prob. 20, 1877-1892.
    • (1992) Ann. Prob. , vol.20 , pp. 1877-1892
    • De La Peña, V.1
  • 6
    • 0000566943 scopus 로고
    • Decoupling inequalities for the tail probabilities of multivariate U-statistics
    • de la Peña, V., and Montgomery-Smith, S. (1995). Decoupling inequalities for the tail probabilities of multivariate U-statistics. Ann. Prob. 23, 806-816.
    • (1995) Ann. Prob. , vol.23 , pp. 806-816
    • De La Peña, V.1    Montgomery-Smith, S.2
  • 7
    • 0011507598 scopus 로고
    • An extension of the law of the iterated logarithm to variables without variance
    • Feller, W. (1968). An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech. 18, 343-355.
    • (1968) J. Math. Mech. , vol.18 , pp. 343-355
    • Feller, W.1
  • 8
    • 0041028537 scopus 로고
    • On Hoffmann-Jørgensen's inequality for U-processes, Birkhäuser, Boston
    • Giné, E., and Zinn, J. (1992a). On Hoffmann-Jørgensen's inequality for U-processes, Birkhäuser, Boston, Probability in Banach Spaces 8, 80-91.
    • (1992) Probability in Banach Spaces , vol.8 , pp. 80-91
    • Giné, E.1    Zinn, J.2
  • 9
    • 0001436898 scopus 로고
    • Marcinkiewicz type laws of large numbers and convergence of moments for U-statistics, Birkhäuser, Boston
    • Giné, E., and Zinn, J. (1992b). Marcinkiewicz type laws of large numbers and convergence of moments for U-statistics, Birkhäuser, Boston, Probability in Banach Spaces 8, 273-291.
    • (1992) Probability in Banach Spaces , vol.8 , pp. 273-291
    • Giné, E.1    Zinn, J.2
  • 10
    • 0001140647 scopus 로고
    • A remark on convergence in distribution of U-statistics
    • Giné, E., and Zinn, J. (1994). A remark on convergence in distribution of U-statistics. Ann. Prob. 22, 117-125.
    • (1994) Ann. Prob. , vol.22 , pp. 117-125
    • Giné, E.1    Zinn, J.2
  • 12
    • 0000704629 scopus 로고
    • The bounded law of the iterated logarithm for the weighted empirical distribution process in the non i.i.d. case
    • Marcus, M. B., and Zinn, J. (1984). The bounded law of the iterated logarithm for the weighted empirical distribution process in the non i.i.d. case. Ann. Prob. 12, 335-360.
    • (1984) Ann. Prob. , vol.12 , pp. 335-360
    • Marcus, M.B.1    Zinn, J.2
  • 13
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    • Strong law of large numbers for U-statistics
    • Rutgers Technical Report No. 94-006. (to appear)
    • Zhang, C.-H. (1994). Strong law of large numbers for U-statistics. Rutgers Technical Report No. 94-006. Ann. Prob. (to appear).
    • (1994) Ann. Prob.
    • Zhang, C.-H.1


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