Sharp Khinchin-type inequalities for symmetric discrete uniform random variables

Havrilla, Alex; Tkocz, Tomasz

doi:10.1007/s11856-021-2244-8

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…. , 0) for Gaussian mixtures (see [1,10]), or for the Rademacher distribution with a large atom at 0 (see Theorem 4 and Remark 14 in [16]).…”

Section: Discussionmentioning

confidence: 99%

Distributional stability of the Szarek and Ball inequalities

Eskenazis¹,

Nayar²,

Tkocz³

2023

Preprint

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We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a 1/ √ 2 fraction of their total ℓ2-mass. We also show a similar extension of the probabilistic formulation of Ball's cube slicing inequality (1986). These results establish the distributional stability of these optimal Khinchin-type inequalities. The underpinning to such estimates is the Fourier-analytic approach going back to Haagerup (1981).

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“…. , 0) for Gaussian mixtures (see [1,10]), or for the Rademacher distribution with a large atom at 0 (see Theorem 4 and Remark 14 in [16]).…”

Section: Discussionmentioning

confidence: 99%

Distributional stability of the Szarek and Ball inequalities

Eskenazis¹,

Nayar²,

Tkocz³

2023

Preprint

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“…This would also be the case for the Gaussian distribution since there is an equivalence between the two distributions (Ledoux & Talagrand, 2013). Other symmetric distributions satisfying a Khintchine‐type inequality could be considered, such as symmetric discrete uniform random variables (Havrilla & Tkocz, 2019), but

B_{2 p}

and the resulting confidence region would need to be adjusted accordingly.…”

Section: Analytic Wild Bootstrap Confidence Regionsmentioning

confidence: 99%

Nonparametric confidence regions via the analytic wild bootstrap

Burak

Kashlak

2022

Can J Statistics

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The wild bootstrap is a nonparametric tool that can be used to estimate a sampling distribution in the presence of heteroscedastic errors. In particular, the wild bootstrap enables us to compute confidence regions for regression parameters under non-i.i.d. models. While the wild bootstrap may perform well in these settings, its obvious drawback is a lack of computational efficiency. The wild bootstrap requires a large number of bootstrap replications, making the use of this tool impractical when dealing with big data. We introduce the analytic wild bootstrap (ANWB), which provides a nonparametric alternative way of constructing confidence regions for regression parameters. The ANWB is superior to the wild bootstrap from a computational standpoint while exhibiting similar finite-sample performance. We report simulation results for both least squares and ridge regression. Additionally, we test the ANWB on a real dataset and compare its performance with that of other standard approaches.

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“…This is always possible since is finite dimensional. However, establishing Khintchine-type inequalities is, in general, a nontrivial task (see [7, 8, 12, 15]).…”

Section: Examples and Applicationsmentioning

confidence: 99%