Arbeitspapier
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors with- out any restriction on the covariance matrices. We also establish an anti-concentration inequality for the maximum of a Gaussian random vector, which derives a useful upper bound on the Lévy concentration function for the Gaussian maximum. The bound is dimension-free and applies to vectors with arbitrary covariance matrices. This anti-concentration in- equality plays a crucial role in establishing bounds on the Kolmogorov distance between maxima of Gaussian random vectors. These results have immediate applications in mathematical statistics. As an example of application, we establish a conditional multiplier central limit theorem for maxima of sums of independent random vectors where the dimension of the vectors is possibly much larger than the sample size.
- Language
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Englisch
- Bibliographic citation
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Series: cemmap working paper ; No. CWP40/16
- Classification
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Wirtschaft
- Subject
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Slepian inequality
anti-concentration
Lévy concentration function
maximum of Gaussian random vector
conditional multiplier central limit theorem
- Event
-
Geistige Schöpfung
- (who)
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Chernozhukov, Victor
Chetverikov, Denis
Kato, Kengo
- Event
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Veröffentlichung
- (who)
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Centre for Microdata Methods and Practice (cemmap)
- (where)
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London
- (when)
-
2016
- DOI
-
doi:10.1920/wp.cem.2016.4016
- Handle
- Last update
-
10.03.2025, 11:41 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Chernozhukov, Victor
- Chetverikov, Denis
- Kato, Kengo
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2016
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