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Two–Sided Bounds for PDF’s Maximum of a Sum of Weighted Chi-square Variables

P. 178–189.
Bobkov S., Naumov A., Ulyanov V. V.

Two–sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence on the parameters of the sum and differ only in absolute constants. The estimates obtained will be useful, in particular, when comparing two Gaussian random elements in a Hilbert space and in multidimensional central limit theorems, including the infinite-dimensional case.

Language: English
DOI
Text on another site
Keywords: weighted sumsGaussian elementchi-square variable
Publication based on the results of:
Uncertainty quantification in machine learning algorithms (2021)

In book

Recent Developments in Stochastic Methods and Applications: ICSM-5, Moscow, Russia, November 23–27, 2020, Selected Contributions
Vol. 371. , Springer, 2021.
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