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Lopes, Miles E.; Lin, Zhenhua; Müller, Hans-Georg

Bootstrapping max statistics in high dimensions: near-parametric rates under weak variance decay and application to functional and multinomial data. (English) Zbl 1464.62266

Ann. Stat. 48, No. 2, 1214-1229 (2020).
The authors study bootstrap based on Gaussian multipliers for “max-type” statistics of functional data. They show that this Gaussian bootstrap method can approximate the distribution of such statistics with a rate close to the nonparametric rate under some assumptions, e.g. independence of the observed vectors and decaying variances of the components. This has the effect that with high probability, the maximum is attained by one of relatively few components with high variance. Assuming this variance decay, the rate is independent of the number of components \(p\). In a simulation study, the Gaussian multiplier bootstrap is compared to a method based on principal components [H. Choi and M. Reimherr, J. R. Stat. Soc., Ser. B, Stat. Methodol. 80, No. 1, 239–260 (2018; Zbl 1381.62143)].
Reviewer: Martin Wendler (Greifswald)

Cited in 12 Documents

MSC:

62G09 Nonparametric statistical resampling methods
62G15 Nonparametric tolerance and confidence regions
62G05 Nonparametric estimation
62R10 Functional data analysis

Keywords:

bootstrap; high-dimensional statistics; functional data analysis

Citations:

Zbl 1381.62143

Software:

MultinomialCI; GitHub; fregion; fda (R); hdi
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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