A Comparative Study of the Rule of Thumb, Umbiased Cross Validation and the Shearther Jones-Direct Plug-in Approaches of Kernel Density Estimation using Real Life Data


Authors : E.C. Ogwu; H.I. Ojarikre

Volume/Issue : Volume 8 - 2023, Issue 3 - March

Google Scholar : https://bit.ly/3TmGbDi

Scribd : https://bit.ly/3zvkBU7

DOI : https://doi.org/10.5281/zenodo.7797387

Abstract : An important measure of the performance of any statistical method is how well it performs in practice especially using real life data. This work has compared the performance of different approaches of kernel density estimation (KDE) for several real data sets, the rule of thumb (NRD0), unbiased cross validation (UCV), and the Sheather Jones direct plug-in (SJ-DPI) approaches were considered. The data set examined includes, the daily closing prices of the Nigerian exchange (NGE), Coca-cola (KO) and NASDAQ stock data for a period of 1year, starting from October 31st 2021 to September 30th 2022. In this work we obtained the kernel density estimation of the data sets using the UCV, NRD0 and SJ-DPI approaches, we further compared the performances of each of the above approaches in terms of the resulting KDE plots and the integrated square error (ISE). We found out that the SJDPI approach produced the best KDE plot for the studied data sets and that the SJ-DPI and NRD0 approaches has the best performance for small and large samples sizes respectively in terms of ISE for the studied data sets. The study therefore suggests that the rule of thumb, unbiased cross validation and the plug-in approaches of KDE should be applied to other real data sets to compare the performance of these approaches. We further suggested that, other approaches of KDE such as the Bayesian approach, the solve the equation approach and the biased cross validation approaches be applied to NASDAQ, NGE, and COCA-COLA data sets in other to compare and investigate the performance of these approaches

Keywords : Kernel density estimation, smoothening parameter, rule of thumb, unbiased cross validation, direct plug-in,integrated square error

An important measure of the performance of any statistical method is how well it performs in practice especially using real life data. This work has compared the performance of different approaches of kernel density estimation (KDE) for several real data sets, the rule of thumb (NRD0), unbiased cross validation (UCV), and the Sheather Jones direct plug-in (SJ-DPI) approaches were considered. The data set examined includes, the daily closing prices of the Nigerian exchange (NGE), Coca-cola (KO) and NASDAQ stock data for a period of 1year, starting from October 31st 2021 to September 30th 2022. In this work we obtained the kernel density estimation of the data sets using the UCV, NRD0 and SJ-DPI approaches, we further compared the performances of each of the above approaches in terms of the resulting KDE plots and the integrated square error (ISE). We found out that the SJDPI approach produced the best KDE plot for the studied data sets and that the SJ-DPI and NRD0 approaches has the best performance for small and large samples sizes respectively in terms of ISE for the studied data sets. The study therefore suggests that the rule of thumb, unbiased cross validation and the plug-in approaches of KDE should be applied to other real data sets to compare the performance of these approaches. We further suggested that, other approaches of KDE such as the Bayesian approach, the solve the equation approach and the biased cross validation approaches be applied to NASDAQ, NGE, and COCA-COLA data sets in other to compare and investigate the performance of these approaches

Keywords : Kernel density estimation, smoothening parameter, rule of thumb, unbiased cross validation, direct plug-in,integrated square error

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