Statistical Topology Using the Nonparametric Density Estimation and Bootstrap Algorithm

Statistical Topology via Morse Theory Persistence and Nonparametric Estimation

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation procedure can then be evaluated using the bottleneck distance between the estimated persistent homology and the true persistent homology. The connection to sta...

Nonparametric Density Estimation using Wavelets

Here the problem of density estimation using wavelets is considered. Nonparametric wavelet density estimators have recently been proposed and seem to outperform classical estimators in representing discontinuities and local oscillations. The purpose of this paper is to give a review of different types of wavelet density estimators proposed in the literature. Properties, comparisons with classic...

Crowdsourced Nonparametric Density Estimation Using Relative Distances

In this paper we address the following density estimation problem: given a number of relative similarity judgements over a set of itemsD, assign a density value p(x) to each item x ∈ D. Our work is motivated by human computing applications where density can be interpreted e.g. as a measure of the rarity of an item. While humans are excellent at solving a range of different visual tasks, assessi...

Sequential nonparametric density estimation

Nonparametric volatility density estimation

B E RT VA N E S , P E T E R S P R E I J 1 and HARRY VAN ZANTEN 2 Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands. E-mail: [email protected]; [email protected] Division of Mathematics and Computer Science, Faculty of Sciences, Free University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands...

Nonparametric estimation of the mixing density using polynomials

We consider the problem of estimating the mixing density f from n i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the hidden variable is not bounded to a finite set but is spread out over a given interval. An orthogonal series estimator of the mixing density f is obtained as follow...