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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 6

Sobolev Convergence of Empirical Bernstein Copulas

Sundusit Saekow
Santi Tasena
Pages
1845–1858
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The result suggests a nonlinear relationship between the dust density in Chiang Mai, Thailand and the temperature and the humidity level.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we prove that Bernstein estimator always converges to the true copula under Sobolev distances.
📊
Key Findings & Data:The rate of convergences is provided in case the true copula has bounded second order derivatives.
💡
Conclusion & Impact:The result suggests a nonlinear relationship between the dust density in Chiang Mai, Thailand and the temperature and the humidity level.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bernstein estimator · copula · empirical

Abstract

In this work, we prove that Bernstein estimator always converges to the true copula under Sobolev distances. The rate of convergences is provided in case the true copula has bounded second order derivatives. Simulation study has also been done for Clayton copulas. We then use this estimator to estimate measures of complete dependence for weather data. The result suggests a nonlinear relationship between the dust density in Chiang Mai, Thailand and the temperature and the humidity level.

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Cite This Article

Saekow, S., Tasena, S. (2022). Sobolev Convergence of Empirical Bernstein Copulas. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1845–1858. https://ajindex.com/articles/529715

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