On nonparametric estimation of density level sets

Adaptive Hausdorff Estimation of Density Level Sets

Hausdorff accurate estimation of density level sets is relevant in applications where a spatially uniform mode of convergence is desired to ensure that the estimated set is close to the target set at all points. The minimax optimal rate of error convergence for the Hausdorff metric is known to be (n/ logn) for level sets with Lipschitz boundaries, where the parameter α characterizes the regular...

Notes On Nonparametric Density Estimation

Univariate Density Estimation via Numerical Derivatives Consider the problem of estimating the density function f(x) of a scalar, continuously-distributed i.i.d. sequence xi at a particular point x. If the density f is in a known parametric family (e.g., Gaussian), estimation of the density reduces to estimation of the finite-dimensional parameters that characterize that particular density in t...

Sequential nonparametric density estimation

Nonparametric Confidence Sets for Density

We present a method for constructing nonparametric confidence sets for density functions based on an approach due to Beran and Dümbgen (1998). We expand the density in an appropriate basis and we estimate the basis coefficients by using linear shrinkage methods. We then find the limiting distribution of an asymptotic pivot based on the quadratic loss function. Inverting this pivot yields a conf...

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...