38 citations · 121 across the 45 of their papers we have counts for
5 papers · 2 filters
Between Chebyshev and Cantelli
Iosif Pinelis
A family of exact upper bounds interpolating between Chebyshev's and Cantelli's is presented.
Best possible bounds of the von Bahr--Esseen type
Iosif Pinelis
The well-known von Bahr--Esseen bound on the absolute th moments of martingales with is extended to a large class of moment functions, and now with a best possible c…
An asymptotically Gaussian bound on the Rademacher tails
Iosif Pinelis
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent t…
Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing
Iosif Pinelis
The main results imply that the probability P(\ZZ\in A+þ) is Schur-concave/Schur-convex in (þ_1^2,\dots,þ_k^2) provided that the indicator function of a set A in \R^k is so, respec…
Exact lower bounds on the exponential moments of Winsorized and truncated random variables
Iosif Pinelis
Exact lower bounds on the exponential moments of min(y,X) and XI{X<y} are provided given the first two moments of a random variable X. These bounds are useful in work on large devi…