Exact lower and upper bounds for shifts of Gaussian measures

05/19/2022
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by   Iosif Pinelis, et al.
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Exact upper and lower bounds on the ratio š–¤w(š—-šÆ)/š–¤w(š—) for a centered Gaussian random vector š— in ā„^n, as well as bounds on the rate of change of š–¤w(š—-tšÆ) in t, where wā„^nā†’[0,āˆž) is any even unimodal function and šÆ is any vector in ā„^n. As a corollary of such results, exact upper and lower bounds on the power function of statistical tests for the mean of a multivariate normal distribution are given.

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