Incomplete U-statistics of permanent design

Journal of Nonparametric Statistics

Volumn 15, Issue 2, 2003, Pages 221-236

  Rempala, Grzegorz ^a   Wesolowski, Jacek ^b  

^a UNIVERSITY OF LOUISVILLE   (United States)

^b WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Incomplete U statistics; Minimum variance designs; Random permanents; Relative efficiency

Indexed keywords

EID: 0037832207     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/1048525031000089284     Document Type: Article

References (22)

1. Blom, G. (1976). Some properties of incomplete U-statistics. Biometrika, 63 (3), 573-580.
2. Brown, B. M. and Kildea, D. G. (1978). Reduced U-statistics and the Hodges-Lehmann estimator. Ann. Statist., 6(4), 828-835.
3. Enqvist, E. (1985). A note on incomplete U-statistics for stationary absolutely regular processes. Contributions to Probability and Statistics in Honour of Gunnar Blom. University of Lund, Lund, Germany, pp. 97-103.
4. Frees, E. W. (1989). Infinite order U-statistics. Scand. J. Statist., 16(1), 29-45.
5. Giné, E., Kwapień, S., Latala, R. and Ziun, J. (2001). The LIL for canonical U-statistics of order 2. Ann, Probability, 29(1), 520-557.
6. Giné, E. and Zinn, J. (1994). A remark on convergence in distribution of U-statistics. Ann, Probab., 22(1), 117-125.
7. Györfi, L., Härdle, W., Sarda, P. and Vieu, P. (1989). Nonparametric Curve Estimation from Time Series. SpringerVerlag, Berlin.
8. Herrndorf, N. (1986). An invariance principle for reduced U-statistics. Metrika, 33(3-4), 179-188.
9. Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Ann. Math. Statistics, 19, 293-325.
10. Janson, S. (1984). The asymptotic distributions of incomplete U-statistics, Z. Wahrsch. Verw. Gebiete, 66(4), 495-505.
11. Janson, S. (1994). The numbers of spanning trees, Hamilton cycles and perfect matchings in a random graph Combin. Probab. Comput., 3(1), 97-126.
12. Korolyuk, V S. and Borovskikh, Y. V (1992). Random permanents and symmetric statistics. Probability Theory and Mathematical Statistics (Kiev, 1991). World Sci. Publishing, River Edge, NJ, pp. 176-187.
13. Latala, R. and Zinn, J. (1999). Necessary and sufficient conditions for SLLN for U-statistics. Ann. Probability, 28(4), 1908-1924.
14. Lee, A. J. (1982). On incomplete U-statistics having minimum variance. Austral. J. Statist., 24(3), 275-282.
15. Lee, A. J. (1990). U-statistics. Theory and Practice, Volume 110 of Statistics; Textbooks and Monographs. Marcel Dekker Inc., New York.
16. Minc, H. (1978). Permanents. Encyclopedia of Mathematics and its Applications, Vol. 6. Addison-Wesley Publishing Co., Reading, Mass (With a foreword by Marvin Marcus).
17. Nowicki, K. and Wierman, J. C. (1988). Subgraph counts in random graphs using incomplete U-statistics methods. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986), Vol. 72, pp. 299-310.
18. Politis, D. N. and Romano, J. P. (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist., 22(4), 2031-2050.
19. Rempala, G. (1998). Strong law of large numbers for U-statistics of varying order. Statist. Probab. Lett., 39(3), 263-270.
20. Rempala, G. and Wesobwski, J. (1999). Asymptotic behavior of random permanents. Statist. Probab. Lett., 45, 149-158.
21. Székely, G. J. (1982). A limit theorem for elementary symmetric polynomials of independent random variables. Z. Wahrsch. Verw. Gebiete, 59(3), 355-359.
22. van Es, A. J. and Helmers, R. (1988). Elementary symmetric polynomials of increasing order. Probab. Theory Related Fields, 80(1), 21-35.