Arbeitspapier
Gaussian approximation of suprema of empirical processes
We develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the supremum norm. We prove an abstract approximation theorem that is applicable to a wide variety of problems, primarily in statistics. In particular, the bound in the main approximation theorem is non-asymptotic and the theorem does not require uniform boundedness of the class of functions. The proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors, the proof of which depends on an effective use of Stein's method for normal approximation, and some new empirical process techniques. We study applications of this approximation theorem to local empirical processes and series estimation in nonparametric regression where the classes of functions change with the sample size and are not Donsker-type. Importantly, our new technique is able to prove the Gaussian approximation for the supremum type statistics under weak regularity conditions, especially concerning the bandwidth and the number of series functions, in those examples.
- Language
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Englisch
- Bibliographic citation
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Series: cemmap working paper ; No. CWP75/13
- Classification
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Wirtschaft
- Event
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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)
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2013
- DOI
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doi:10.1920/wp.cem.2013.7513
- Handle
- Last update
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10.03.2025, 11:45 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
- 2013
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Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
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Simultaneous inference for best linear predictor of the conditional average treatment effect and other structural functions
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Quantile models with endogeneity
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Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
Uniform inference in high-dimensional gaussian graphical models
Simultaneous inference for best linear predictor of the conditional average treatment effect and other structural functions
Posterior inference in curved exponential families under increasing dimensions
Inference for extremal conditional quantile models, with an application to market and birthweight risks
Quantile models with endogeneity