In this paper, we aim to explore the speed of convergence of the Wasserstein distance between stable cumulative distribution functions and their empirical counterparts. The theoretical results are compared with the results provided by simulations. The need to use simulations is explained by the fact that all the theoretical results which relate to the speed of convergence of the Wasserstein Met...

in this paper, we generalize some results of chandra and goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). furthermore, we give baum and katz’s [1] type results on estimate for the rate of convergence in these laws.

with n = N/V the number density of swimmers. This is nonzero (and might diverge) in the limit V → ∞, reflecting the cumulative effect of multiple swimmers. Note that this expression is exact, within the problem assumptions: it doesn’t even require N to be large. It is not at all clear that (4) leads to diffusive behavior, but it does [2–4]: the “support” of the drift function ∆(η, t) typically ...

In many practical applications, data about an unknown continuous distribution arise in a grouped form. For these cases, estimation of population entropies and divergences must be done by means of their sample discretized estimates. In this paper, the problem of loss of information due to the discretization of the data is studied for (h, )-entropies and R^-diveigences. Quadratic convergence t...

The performance of individual agents in a group depends critically on the quality of information available to it about local and global goals and resources. In general it is assumed that the more accurate and up-to-date the available information , the better is the expected performance of the individual and the group. This conclusion can be challenged in a number of scenarios. We investigate th...

In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.

Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R give rise to walks with the fastest convergence.

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of t...

University of California at Berkeley and The Hebrew University of Jerusalem ∗†We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the minimax rate of convergence on suitable function spaces, while, at the same time, when “plugged-in”, estimate efficiently (at a rate of n−1/2 with the best constant) many function...