Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls
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Upper bounds for the closeness of two centered Gaussian measures in the class of balls in a separable Hilbert space are obtained. The bounds are optimal with respect to the dependence on the spectra of the covariance operators of the Gaussian measures. The inequalities cannot be improved in the general case.
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- 6.A. Naumov, V. Spokoiny, and V. Ulyanov, “Bootstrap confidence sets for spectral projectors of sample covariance” (2017). arXiv:1703.00871.Google Scholar
- 7.A. Naumov, V. Spokoiny, and V. Ulyanov, “Confidence sets for spectral projectors of covariance matrices,” Dokl. Math. 98 (2018).Google Scholar
- 10.V. V. Ulyanov, “On Gaussian measure of balls in H,” in Frontiers in Pure and Applied Probability, Proceedings of the 4th Russian–Finnish Symposium on Probability Theory and Mathematical Statistics (TVP Science, Moscow, 1995).Google Scholar
- 11.K. Chung, A Course in Probability Theory, 3rd ed. (Academic, San Diego, CA, 2001).Google Scholar
- 12.F. Götze, A. Naumov, V. Spokoiny, and V. Ulyanov, “Large ball probabilities, Gaussian comparison and anticoncentration”, Bernoulli 25 (2019). arXiv:1708.08663v2.Google Scholar