The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.
Celem niniejszego artykułu jest przedstawienie kwantylowych estymatorów krzywych Lorentza. Pokazano punktową zgodność tych estymatorów oraz ich asymptotyczną normalność. Badań jest także efektywność zaproponowanych estymatorów metodami symulacji komputerowych.
EN
Estimators of quantile versions of the Lorenz curve are proposed. The pointwise consistency and asymptotic normality of the estimators is proved. The efficiency of the estimators is also studied in simulations
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