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Article: Bootstrap confidence regions based on M-estimators under nonstandard conditions
Title | Bootstrap confidence regions based on M-estimators under nonstandard conditions |
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Authors | |
Issue Date | 2020 |
Publisher | Institute of Mathematical Statistics. The Journal's web site is located at https://imstat.org/journals-and-publications/annals-of-statistics/ |
Citation | The Annals of Statistics, 2020, v. 48 n. 1, p. 274-299 How to Cite? |
Abstract | Suppose that a confidence region is desired for a subvector θ of a multidimensional parameter ξ=(θ,ψ), based on an M-estimator ξ^n=(θ^n,ψ^n) calculated from a random sample of size n. Under nonstandard conditions ξ^n often converges at a nonregular rate rn, in which case consistent estimation of the distribution of rn(θ^n−θ), a pivot commonly chosen for confidence region construction, is most conveniently effected by the m out of n bootstrap. The above choice of pivot has three drawbacks: (i) the shape of the region is either subjectively prescribed or controlled by a computationally intensive depth function; (ii) the region is not transformation equivariant; (iii) ξ^n may not be uniquely defined. To resolve the above difficulties, we propose a one-dimensional pivot derived from the criterion function, and prove that its distribution can be consistently estimated by the m out of n bootstrap, or by a modified version of the perturbation bootstrap. This leads to a new method for constructing confidence regions which are transformation equivariant and have shapes driven solely by the criterion function. A subsampling procedure is proposed for selecting m in practice. Empirical performance of the new method is illustrated with examples drawn from different nonstandard M-estimation settings. Extension of our theory to row-wise independent triangular arrays is also explored. |
Persistent Identifier | http://hdl.handle.net/10722/275752 |
ISSN | 2023 Impact Factor: 3.2 2023 SCImago Journal Rankings: 5.335 |
DC Field | Value | Language |
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dc.contributor.author | Lee, SMS | - |
dc.contributor.author | Yang, P | - |
dc.date.accessioned | 2019-09-10T02:48:58Z | - |
dc.date.available | 2019-09-10T02:48:58Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | The Annals of Statistics, 2020, v. 48 n. 1, p. 274-299 | - |
dc.identifier.issn | 0090-5364 | - |
dc.identifier.uri | http://hdl.handle.net/10722/275752 | - |
dc.description.abstract | Suppose that a confidence region is desired for a subvector θ of a multidimensional parameter ξ=(θ,ψ), based on an M-estimator ξ^n=(θ^n,ψ^n) calculated from a random sample of size n. Under nonstandard conditions ξ^n often converges at a nonregular rate rn, in which case consistent estimation of the distribution of rn(θ^n−θ), a pivot commonly chosen for confidence region construction, is most conveniently effected by the m out of n bootstrap. The above choice of pivot has three drawbacks: (i) the shape of the region is either subjectively prescribed or controlled by a computationally intensive depth function; (ii) the region is not transformation equivariant; (iii) ξ^n may not be uniquely defined. To resolve the above difficulties, we propose a one-dimensional pivot derived from the criterion function, and prove that its distribution can be consistently estimated by the m out of n bootstrap, or by a modified version of the perturbation bootstrap. This leads to a new method for constructing confidence regions which are transformation equivariant and have shapes driven solely by the criterion function. A subsampling procedure is proposed for selecting m in practice. Empirical performance of the new method is illustrated with examples drawn from different nonstandard M-estimation settings. Extension of our theory to row-wise independent triangular arrays is also explored. | - |
dc.language | eng | - |
dc.publisher | Institute of Mathematical Statistics. The Journal's web site is located at https://imstat.org/journals-and-publications/annals-of-statistics/ | - |
dc.relation.ispartof | The Annals of Statistics | - |
dc.title | Bootstrap confidence regions based on M-estimators under nonstandard conditions | - |
dc.type | Article | - |
dc.identifier.email | Lee, SMS: smslee@hku.hk | - |
dc.identifier.authority | Lee, SMS=rp00726 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.hkuros | 303339 | - |
dc.identifier.hkuros | 316294 | - |
dc.identifier.volume | 48 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 274 | - |
dc.identifier.epage | 299 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0090-5364 | - |