Academic literature on the topic 'Epanechnikov kernel'

Precisely determining agricultural land abandonment (ALA) in an area is still difficult, even with recent progress in data collection and analysis. It is especially difficult in fragmented areas that need more tailor-made methods. The aim of this research was to determine ALA using airborne laser scanning (ALS) data, which are available in Poland with 4 to 6 points per square metre resolution. ALS data were processed into heat maps and modified with chosen kernel functions: triweight and Epanechnikov. The results of ALS data processing were compared to the control method, i.e., visual interpretation of an orthophotomap. This study shows that ALS data modelled with kernel functions allow for a good identification of ALA. The accuracy of results shows 82% concordance as compared to the control method. When comparing triweight and Epanechnikov functions, higher accuracy was achieved when using the triweight function. The research shows that ALS data processing is a promising method of detection of ALA and could provide an alternative to well-known methods such as the analysis of satellite images.

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 [1] 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 [6]. 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.