Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

López, Juan Carlos Cortés; Sanz, Marc Jornet

doi:10.3390/mca25020033

Cited by 7 publications

(5 citation statements)

References 9 publications

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“…It should also be noted that the values of the coefficients of quantile regressions (Table 14) depend on the type of function in Formula ( 15) and the definition of the parameter h (bandwidth), but the quality of the obtained models should be checked using the Student's test and the p-value [62].…”

Section: Discussionmentioning

confidence: 99%

Global Digital Convergence: Impact of Cybersecurity, Business Transparency, Economic Transformation, and AML Efficiency

Kuzior

Vasylieva²,

Kuzmenko³

et al. 2022

Journal of Open Innovation: Technology, Market, and Complexity

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The article substantiates the existence of convergence processes in the field of digitization of countries, taking into account the number of Internet users; people with advanced skills; and indicators of infrastructure (network coverage, population covered by at least a 3G mobile network, population covered by at least a 4G mobile network), access (access to ICT at home, active mobile broadband subscriptions, fixed broadband subscriptions), enablers (fixed broadband over 10 Mbps, mobile data and voice basket, high consumption) and barriers (improved broadband access from 256 kbps to 2 Mbps and from 2 Mbps to 10 Mbps mobile data and voice basket, low consumption) of digital development. The methodological basis for determining the sigma convergence of digitization processes is the coefficient of variation. The values of the coefficient of variation confirmed the high level of convergence between the studied countries in terms of the degree of use of the Internet for conducting digital transactions. The developed econometric model, which describes the influence of statistically significant integral indicators of the national cybersecurity level, ease of doing business, and the anti-money laundering index on the country’s digital development level, made it possible to determine the average trend of dependence on the level of digital development. One hundred four countries were considered for the analysis. The conducted study of the impact of digitalization on economic transformations based on developed quantile regressions made it possible to analyze exactly how the level of digital development for countries with a high level of digitalization and for countries with a low level of digitalization development depends on the value of the national cybersecurity indicator and the ease of doing business, and which countries have the least resistance to the risk factors of their involvement in fraudulent schemes for the purpose of legalizing criminal income.

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Section: Discussionmentioning

confidence: 99%

Global Digital Convergence: Impact of Cybersecurity, Business Transparency, Economic Transformation, and AML Efficiency

Kuzior

Vasylieva²,

Kuzmenko³

et al. 2022

Journal of Open Innovation: Technology, Market, and Complexity

View full text Add to dashboard Cite

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“…For all of the samples, the bandwidth was set to 0.2. , Linear regression models were developed for particle mass and number data obtained from all of the scenarios as most of the data seemed to have a strong association with such models. Assuming a prolonged strong association of the response (i.e., particle mass and number) and the cycle, the models were used to predict the mass and number of microplastics after repeated use of plastic chopping boards if the analysis of variance (ANOVA) test was statistically significant ( p < 0.05).…”

Section: Methodsmentioning

confidence: 99%

Cutting Boards: An Overlooked Source of Microplastics in Human Food?

Yadav

Khan

Quadir

et al. 2023

Environ. Sci. Technol.

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Plastic cutting boards are a potentially significant source of microplastics in human food. Thus, we investigated the impact of chopping styles and board materials on microplastics released during chopping. As chopping progressed, the effects of chopping styles on microplastic release became evident. The mass and number of microplastics released from polypropylene chopping boards were greater than polyethylene by 5−60% and 14−71%, respectively. Chopping on polyethylene boards was associated with a greater release of microplastics with a vegetable (i.e., carrots) than chopping without carrots. Microplastics showed a broad, bottom-skewed normal distribution, dominated by <100 μm spherical-shaped microplastics. Based on our assumptions, we estimated a per-person annual exposure of 7.4−50.7 g of microplastics from a polyethylene chopping board and 49.5 g of microplastics from a polypropylene chopping board. We further estimated that a person could be exposed to 14.5 to 71.9 million polyethylene microplastics annually, compared to 79.4 million polypropylene microplastics from chopping boards. The preliminary toxicity study of the polyethylene microplastics did not show adverse effects on the viability of mouse fibroblast cells for 72 h. This study identifies plastic chopping boards as a substantial source of microplastics in human food, which requires careful attention.

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“…Let f be a sufficiently smooth and bounded density function, and let k(t) satisfy the conditions in Eq. (17).…”

Section: Error Criterionmentioning

confidence: 99%

“…The family of second-order classical beta polynomial kernels is an important family of kernel functions used in kernel density estimation for data visualization [20]. These kernels provide smoother estimates with more derivatives as the degree of the function increases, and they have been widely used in various applications of KDE [17,25,26]. They offer flexibility in shaping the density estimate and can capture different patterns and features in the data.…”

Section: A Family Of Second-order Classical Beta Polynomial Kernelsmentioning

confidence: 99%

“…NKDE is a robust and elegant smoothing method used in statistical and related problems [12,13]. It finds applications in various fields, such as econometrics [14], insurance [15], climatology with emphasis on typhoon genesis [16], differential equations [17], and several others. KDE is a widely employed nonparametric technique used in statistics, data analysis, and machine learning to estimate the probability density function (PDF) of a random variable [6,18].…”

Section: Introductionmentioning

confidence: 99%

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On the fourth-order hybrid beta polynomial kernels in kernel density estimation

Afere

2024

J. Nig. Soc. Phys. Sci.

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This paper introduces a novel family of fourth-order hybrid beta polynomial kernels tailored for statistical analysis. The efficacy of these kernels is evaluated using two principal performance metrics: asymptotic mean integrated squared error (AMISE) and kernel efficiency. Comprehensive assessments were conducted using both simulated and real-world datasets, enabling a thorough comparison with conventional fourth-order polynomial kernels. The evaluation process entailed computing AMISE and efficiency metrics for both the hybrid and classical kernels. Consistently, the results illustrated the superior performance of the hybrid kernels over their classical counterparts across diverse datasets, underscoring the robustness and effectiveness of the hybrid approach. By leveraging these performance metrics and conducting evaluations on simulated and real world data, this study furnishes compelling evidence supporting the superiority of the proposed hybrid beta polynomial kernels. The heightened performance, evidenced by lower AMISE values and elevated efficiency scores, strongly advocates for the adoption of the proposed kernels in statistical analysis tasks, presenting a marked improvement over traditional kernels.

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Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

Cited by 7 publications

References 9 publications

Global Digital Convergence: Impact of Cybersecurity, Business Transparency, Economic Transformation, and AML Efficiency

Global Digital Convergence: Impact of Cybersecurity, Business Transparency, Economic Transformation, and AML Efficiency

Cutting Boards: An Overlooked Source of Microplastics in Human Food?

On the fourth-order hybrid beta polynomial kernels in kernel density estimation

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