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: email@example.com
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.
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