Nonparametric curve estimation and bootstrap bandwidth selection

Abstract

Over the last four decades, the bootstrap method has been considered so as to define data-driven bandwidth selectors for nonparametric curve estimation. An extensive and updated review of bootstrap methods used to select the smoothing parameter for the nonparametric estimation of several curves has been carried out. Different data generating processes have been profoundly reviewed, such as the classical independent and identically distributed setup as well as dependent, censored, length-biased, grouped, missing or directional data, among others. Several curves have also been considered, such as the density, regression, hazard rate, intensity, latency, incidence, or distribution functions, among many others. It is worth mentioning that there exist situations where Monte Carlo methods are not needed when using the bootstrap for bandwidth selections. This idea has also been exploited to find closed expressions for the bootstrap version of criterion functions for some proxy of the real curve estimator. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling

A new family of kernels from the beta polynomial kernels with applications in density estimation

“…The fundamental concepts in kernel density estimation are kernel function and the smoothness factor or bandwidth. Some research has been geared towards these two concepts, but there is no universally accepted method in all situations; hence new methods are usually initiated [29]. The proposed kernel functions from the polynomial beta family use an exponential progression, where there is a constant common ratio to all the polynomial functions.…”