The study and comparison of one-dimensional kernel estimators – a new approach. Part 2. A hydrology case study

The main purpose of this article is to present the numerical consequences of selected methods of kernel estimation, using the example of empirical data from a hydrological experiment [1, 2]. In the construction of kernel estimators we used two types of kernels – Gaussian and Epanechnikov – and several methods of selecting the optimal smoothing bandwidth (see Part 1), based on various statistical and analytical conditions [3–6]. Further analysis of the properties of kernel estimators is limited to eight characteristic estimators. To assess the effectiveness of the considered estimates and their similarity, we applied the distance measure of Marczewski and Steinhaus [7]. Theoretical and numerical considerations enable the development of an algorithm for the selection of locally most effective kernel estimators