Abstract
It is well known that Efron's bootstrap can fail in settings where the data are heavy tailed and when regularity conditions do not hold. Naturally this applies to weighted bootstrap schemes such as the Bayesian bootstrap. To deal with this, we introduce a Bayesian bootstrap analogue of the m out of n bootstrap. This bootstrap differs from traditional m out of n bootstraps in that all n observations are used in the bootstrap test statistic. Moreover, the method is relatively robust to the selection of m. We establish consistency for the new bootstrap and examine its other useful properties including a connection to the Dirichlet process. Several examples illustrating consistency in settings where the Efron bootstrap fails are given. Further generalizations are suggested.
| Original language | English |
|---|---|
| Pages (from-to) | 788-801 |
| Number of pages | 14 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 139 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1 2009 |
| Externally published | Yes |
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Keywords
- Bayesian bootstrap
- Dirichlet process
- Point process
- Stable process
- Sub-sampling
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability
Cite this
An alternative to the m out of n bootstrap. / Ishwaran, Hemant; James, Lancelot F.; Zarepour, Mahmoud.
In: Journal of Statistical Planning and Inference, Vol. 139, No. 3, 01.03.2009, p. 788-801.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An alternative to the m out of n bootstrap
AU - Ishwaran, Hemant
AU - James, Lancelot F.
AU - Zarepour, Mahmoud
PY - 2009/3/1
Y1 - 2009/3/1
N2 - It is well known that Efron's bootstrap can fail in settings where the data are heavy tailed and when regularity conditions do not hold. Naturally this applies to weighted bootstrap schemes such as the Bayesian bootstrap. To deal with this, we introduce a Bayesian bootstrap analogue of the m out of n bootstrap. This bootstrap differs from traditional m out of n bootstraps in that all n observations are used in the bootstrap test statistic. Moreover, the method is relatively robust to the selection of m. We establish consistency for the new bootstrap and examine its other useful properties including a connection to the Dirichlet process. Several examples illustrating consistency in settings where the Efron bootstrap fails are given. Further generalizations are suggested.
AB - It is well known that Efron's bootstrap can fail in settings where the data are heavy tailed and when regularity conditions do not hold. Naturally this applies to weighted bootstrap schemes such as the Bayesian bootstrap. To deal with this, we introduce a Bayesian bootstrap analogue of the m out of n bootstrap. This bootstrap differs from traditional m out of n bootstraps in that all n observations are used in the bootstrap test statistic. Moreover, the method is relatively robust to the selection of m. We establish consistency for the new bootstrap and examine its other useful properties including a connection to the Dirichlet process. Several examples illustrating consistency in settings where the Efron bootstrap fails are given. Further generalizations are suggested.
KW - Bayesian bootstrap
KW - Dirichlet process
KW - Point process
KW - Stable process
KW - Sub-sampling
UR - http://www.scopus.com/inward/record.url?scp=56949105432&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=56949105432&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2008.04.032
DO - 10.1016/j.jspi.2008.04.032
M3 - Article
AN - SCOPUS:56949105432
VL - 139
SP - 788
EP - 801
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 3
ER -