68 citations · 79 across the 19 of their papers we have counts for
19 papers
Semiparametric Statistics and the Spread Inequality
Chris A. J. Klaassen
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen…
A Markovian Gauß\, Inequality for Asymmetric Deviations from the Mode of Symmetric Unimodal Distributions
Chris A. J. Klaassen
For a random variable with a unimodal distribution and finite second moment Gauß\, (1823) proved a sharp bound on the probability of the random variable to be outside a symmetric i…
Inference via the Skewness-Kurtosis Set
Chris A. J. Klaassen, Bert van Es
Kurtosis minus squared skewness is bounded from below by 1, but for unimodal distributions this parameter is bounded by 189/125. In some applications it is natural to compare distr…
Sharp unifying generalizations of Opial's inequality
Chris A. J. Klaassen
Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is pre…
Sharp Inequalities of Bienaymé-Chebyshev and GaußType for Possibly Asymmetric Intervals around the Mean
Roxana A. Ion, Chris A. J. Klaassen, Edwin R. van den Heuvel
Gauß(1823) proved a sharp upper bound on the probability that a random variable falls outside a symmetric interval around zero when its distribution is unimodal with mode at zero.…
Probability Theoretic Generalizations of Hardy's and Copson's Inequality
Chris A. J. Klaassen
A short proof of the classic Hardy inequality is presented for -norms with . Along the lines of this proof a sharpened version is proved of a recent generalization of Hardy…