Downloads
cwp381616.pdf
PDF | 426.8 KB
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian-Stein methods and Gaussian comparison inequalities. The increasing complexity of classes of functions and non-centrality of the processes make the results useful for applications in modern nonparametric statistics (Giné and Nickl [14]), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations.
Authors
Working Paper details
- DOI
- 10.1920/wp.cem.2016.3816
- Publisher
- The IFS
Suggested citation
V, Chernozhukov and D, Chetverikov and K, Kato. (2016). Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings. London: The IFS. Available at: https://ifs.org.uk/publications/empirical-and-multiplier-bootstraps-suprema-empirical-processes-increasing-complexity (accessed: 29 March 2024).
More from IFS
Understand this issue
Gender norms, violence and adolescent girls’ trajectories: Evidence from India
24 October 2022
Spring Budget 2024: What you need to know
7 March 2024
IFS Deputy Director Carl Emmerson made a Fellow of the Academy of Social Sciences
4 March 2024
Policy analysis
IFS Deputy Director Carl Emmerson appointed to the UK Statistics Authority Methodological Assurance Review Panel
14 April 2023
ABC of SV: Limited Information Likelihood Inference in Stochastic Volatility Jump-Diffusion Models
We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Compu- tation which build likelihoods based on limited information.
12 August 2014
Is there really an NHS productivity crisis?
17 November 2023
Academic research
Understanding Society: minimising selection biases in data collection using mobile apps
2 February 2024
Sample composition and representativeness on Understanding Society
2 February 2024
Robust analysis of short panels
8 January 2024