Abstract:
The paper considers the new approach to the reconstruction of the probability density function similarly the averaged shifted histogram method. An algorithm is used Richardson's extrapolation for increasing accuracy. We prove the estimates of the accuracy of the probability density function and its second derivative to choose the optimal settings for smoothing the histogram and kernel estimators and to consider the optimal choice problem of the bandwidth parameter. Presented the results of numerical experiments.
Keywords:
MISE, error estimate, Richardson's extrapolation, Runge's rule, probability density functions estimation, probability density function derivatives, Numerical probabilistic analysis.
Received: 03.06.2016 Received in revised form: 09.09.2016 Accepted: 10.11.2016
Bibliographic databases:
Document Type:
Article
UDC:519.24
Language: English
Citation:
Boris S. Dobronets, Olga A. Popova, “Improving the accuracy of the probability density function estimation”, J. Sib. Fed. Univ. Math. Phys., 10:1 (2017), 16–21
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\by Boris~S.~Dobronets, Olga~A.~Popova
\paper Improving the accuracy of the probability density function estimation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2017
\vol 10
\issue 1
\pages 16--21
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\crossref{https://doi.org/10.17516/1997-1397-2017-10-1-16-21}
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Linking options:
https://www.mathnet.ru/eng/jsfu517
https://www.mathnet.ru/eng/jsfu/v10/i1/p16
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B S Dobronets, O A Popova, “Modeling Under Uncertainty: a Comparison of Approaches”, J. Phys.: Conf. Ser., 1715:1 (2021), 012061
B. S. Dobronets, O. A. Popova, “Vychislitelnye aspekty tsifrovoi ekonomiki”, UBS, 84 (2020), 114–129
B. Dobronets, O. Popova, A. Merko, “Computational probabilistic analysis and transformation method in the earth remote research”, Regional Problems of Earth Remote Sensing (Rpers 2020), E3S Web of Conferences, 223, eds. G. Gennady, M. Noskov, Maglinets, A., EDP Sciences, 2020, 02001
B S Dobronets, O A Popova, “Computational Probabilistic Analysis of Distributional Time Series”, J. Phys.: Conf. Ser., 1680:1 (2020), 012008
Boris Dobronets, Olga Popova, V.B. Kashkin, V. Kharuk, E. Loupian, Y.A. Maglinets, M.V. Noskov, L.G. Sverdlik, G.M. Tsibulśkii, “The Reliability of Numerical Modeling in Remote Sensing Data Analysis”, E3S Web Conf., 149 (2020), 02012
B. S. Dobronets, O. A. Popova, “Computational aspects of probabilistic extensions”, Int. J. Geotech. Earthq., 2019, no. 47, 41–48
O. A. Popova, “Using Richardson extrapolation to improve the accuracy of processing and analyzing empirical data”, Meas. Tech., 62:2 (2019), 111–117
B. Dobronets, O. Popova, “Numerical analysis for problems of remote sensing with random input data”, Regional Problems of Earth Remote Sensing (Rpers 2018), E3S Web of Conferences, 75, eds. G. Tsibulskiy, M. Noskov, E. Lupyan, L. Sverdlik, A. Sagatelian, V. Kharuk, V. Kashkin, EDP Sciences, 2019, 01004
B. S. Dobronets, O. A. Popova, “Improving reliability of aggregation, numerical simulation and analysis of complex systems by empirical data”, XI All-Russian Scientific and Practical Conference (With International Participation) Automation Systems in Education, Science and Production, 2017, IOP Conference Series-Materials Science and Engineering, 354, IOP Publishing Ltd, 2018, 012006
B. S. Dobronets, O. A. Popova, “Piecewise polynomial aggregation as preprocessing for data numerical modeling”, International Conference Information Technologies in Business and Industry 2018, Journal of Physics Conference Series, 1015, IOP Publishing Ltd, 2018, 032028
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