Asymptotics with increasing dimension for robust regression with applications to the bootstrap
A stochastic expansion for MMM-estimates in linear models with many parameters is derived under the weak condition κn1/3(logn)2/3→0κn1/3(logn)2/3→0\kappa n^{1/3}(\log n)^{2/3} \rightarrow 0, where nnn is the sample size and κκ\kappa the maximal diagonal element of the hat matrix. The expansion is u...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1989
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| In: |
The annals of statistics
Year: 1989, Volume: 17, Issue: 1, Pages: 382-400 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176347023 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1176347023 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1176347023 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1176347023 
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| Author Notes: | Enno Mammen |
MARC
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| 520 | |a A stochastic expansion for MMM-estimates in linear models with many parameters is derived under the weak condition κn1/3(logn)2/3→0κn1/3(logn)2/3→0\kappa n^{1/3}(\log n)^{2/3} \rightarrow 0, where nnn is the sample size and κκ\kappa the maximal diagonal element of the hat matrix. The expansion is used to study the asymptotic distribution of linear contrasts and the consistency of the bootstrap. In particular, it turns out that bootstrap works in cases where the usual asymptotic approach fails. | ||
| 650 | 4 | |a bootstrap | |
| 650 | 4 | |a $M$-estimators | |
| 650 | 4 | |a asymptotic normality | |
| 650 | 4 | |a dimension asymptotics | |
| 650 | 4 | |a linear model | |
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