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We prove generalizations of L¨owner’s results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuti...
We show how the mean of a monotone function (dened on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of...
Metric entropy of the class of probability distribution functions on [0,1] with a k-monotone density is studied through its connection with the small ball probability of k-times integrated Brownian mo...
Suppose that a target function f0 : Rd → R is monotonic, namely, weakly increasing, and an original estimate ˆ f of the target function is available, which is not weakly increasing. Many common...

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