A data-driven kernel estimator of the density function

The main purpose of this paper is to provide an effective nonparametric method of kernel estimation of the density function for various specific data. A convex linear combination of the most locally effective known kernel estimators constructed using different approaches allows one to build an estimator that combines the best features of all analysed estimators. The paper presents an original concept for studying the local effectiveness of the kernel estimator of the density function based on the Marczewski-Steinhaus metric. It is shown that none of the applied kernel estimators can be considered globally optimal if local effectiveness is taken into account. The presented numerical calculations were done for experimental data recording groundwater levels on a melioration facility and supported by simulation studies.