Higher order accuracy of the bootstrap method for smooth functionals
In this paper we consider bootstrap of a smooth functional T. We give a simple proof for the higher order accuracy of the bootstrap estimate. In particular, we show that the expectation of a smooth function of the studentised functional is estimated to order $O_{P}(n^{-1})$. Furthermore for symmetri...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1992
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| In: |
Scandinavian journal of statistics
Year: 1992, Volume: 19, Issue: 3, Pages: 255-269 |
| ISSN: | 1467-9469 |
| Online Access: | Verlag, Volltext: http://www.jstor.org/stable/4616243?seq=1#page_scan_tab_contents Verlag, Volltext: http://www.jstor.org/stable/4616243 
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| Author Notes: | E. Mammen |
| Summary: | In this paper we consider bootstrap of a smooth functional T. We give a simple proof for the higher order accuracy of the bootstrap estimate. In particular, we show that the expectation of a smooth function of the studentised functional is estimated to order $O_{P}(n^{-1})$. Furthermore for symmetric functions the rate of convergence increases to $O_{P}(n^{-3/2})$. These results are in agreement with Hall (1986, 1988, 1992), where these rates of convergence have been shown for functionals which are implicit or explicit functions of vector means. |
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| Item Description: | Gesehen am 27.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1467-9469 |