Exact lower and upper bounds for shifts of Gaussian measures
Exact upper and lower bounds on the ratio š¤w(š-šÆ)/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-tšÆ) in t, where wā^nā[0,ā) is any even unimodal function and šÆ 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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