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The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…
Communication-enabled devices routinely carried by individuals have become pervasive, opening unprecedented opportunities for collecting digital metadata about the mobility of large populations. In this paper, we propose a novel methodology…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information,…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of…
This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…