Nonparametric methods provide a flexible framework for estimating the probability density function of random variables without imposing a strict parametric model. By relying directly on observed data, ...

Density estimation is a fundamental component in statistical analysis, aiming to infer the probability distribution of a random variable from a finite sample without imposing restrictive parametric ...

Disclaimer: This Working Paper should not be reported as representing the views of the IMF.The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those ...

In this paper we show how one canimplement in practice the bandwidth selection in deconvolution recursive kernel estimators of a probability density function defined by the stochastic approximation ...

Several papers have recommended the Champernowne distribution to describe operational risk losses. This paper compares the tail performance of the Champernowne transformed kernel density estimator, ...

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based ...

where K 0 (·) is a kernel function, is the bandwidth, n is the sample size, and x i is the i th observation. The KERNEL option provides three kernel functions (K 0): normal, quadratic, and triangular.