38 citations · 121 across the 45 of their papers we have counts for
4 papers · 2 filters
Relations between the first four moments
Iosif Pinelis
Let m_j denote the jth moment of a random variable X. One of the results is the inequality m_3 \leq c m_4^{3/4} with the best possible factor c over all random variables X with a n…
Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities
Iosif Pinelis
For any nonnegative Borel-measurable function f such that f(x)=0 if and only if x=0, the best constant c_f in the inequality E f(X-E X) \leq c_f E f(X) for all random variables X w…
Improved nonuniform Berry--Esseen-type bounds
Iosif Pinelis
New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics. The pro…
Exact bounds on the truncated-tilted mean, with applications
Iosif Pinelis
Exact upper bounds on the Winsorised-tilted mean of a random variable in terms of its first two moments are given. Such results are needed in work on nonuniform Berry--Esseen-type…