Athreya, Krishna B. ; Ghosh, Malay ; Low, Leone Y. ; Sen, Pranab K. (1984) Laws of large numbers for bootstrapped U-statistics Journal of Statistical Planning and Inference, 9 (2). pp. 185-194. ISSN 0378-3758
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037837...
Related URL: http://dx.doi.org/10.1016/0378-3758(84)90019-3
Abstract
For the bootstrapped mean, a strong law of large numbers is obtained under the assumption of finiteness of the rth moment, for some r>1, and a weak law of large numbers is obtained under the finiteness of the first moment. The results are then extended to bootstrapped U-statistics under parallel conditions. Stochastic convergence of the jackknifed estimator of the variance of a bootstrapped U-statistic is proved. The asymptotic normality of the bootstrapped pivot and the bias of the bootstrapped U-statistic are indicated.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Asymptotic Theory; Bootstrap; Laws of Large Numbers; Means; Reversed (sub-) Martriangles; U-statistics; Von Mise's Functionals |
| ID Code: | 1121 |
| Deposited On: | 05 Oct 2010 12:54 |
| Last Modified: | 12 May 2011 10:13 |
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