ITM Web Conf.
Volume 23, 2018XLVIII Seminar of Applied Mathematics
|Number of page(s)||5|
|Published online||07 November 2018|
The study and comparison of one-dimensional kernel estimators – a new approach. Part 1. Theory and methods
Department of Mathematics, Wroclaw University of Environmental and Life Sciences Grunwaldzka 53, 50-357 Wroclaw, Poland
* Corresponding author: firstname.lastname@example.org
In this article we compare and examine the effectiveness of different kernel density estimates for some experimental data. For a given random sample X1, X2, …, Xn we present eight kernel estimators fn of the density function f with the Gaussian kernel and with the kernel given by Epanechnikov  using several methods: Silverman’s rule of thumb, the Sheather–Jones method, cross-validation methods, and other better-known plug-in methods [2–5]. To assess the effectiveness of the considered estimators and their similarity, we applied a distance measure for measurable and integrable functions . All numerical calculations were performed for a set of experimental data recording groundwater level at a land reclamation facility (cf. [7–8]). The goal of the paper is to present a method that allows the study of local properties of the examined kernel estimators.
© The Authors, published by EDP Sciences, 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.