Related papers: Approximating power by weights
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the re- spective state. In this article we ask the question which voting weight guarantees a `fair' representation of…
Forecast combination and model averaging have become popular tools in forecasting and prediction, both of which combine a set of candidate estimates with certain weights and are often shown to outperform single estimates. A data-driven…
Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds \tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…
Consider the family of power divergence statistics based on $n$ trials, each leading to one of $r$ possible outcomes. This includes the log-likelihood ratio and Pearson's statistic as important special cases. It is known that in certain…
To assess the presence of gerrymandering, one can consider the shapes of districts or the distribution of votes. The "efficiency gap," which does the latter, plays a central role in a 2016 federal court case on the constitutionality of…
We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power law probability…
In this study, we propose a generalization of the classic model of liquid democracy that allows fractional delegation of voting weight, while simultaneously allowing for the existence of equilibrium states. Our approach empowers agents to…
When selecting committees based on preferences of voters, a variety of different criteria can be considered. Two natural objectives are maximizing the utilitarian welfare (the sum of voters' utilities) and coverage (the number of…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
We investigate the rate of convergence in the central limit theorem for convex sets. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the…