Year 2019, Volume 48 , Issue 6, Pages 1845 - 1858 2019-12-08

Sobolev Convergence of Empirical Bernstein Copulas

Sundusit SAEKAOW [1] , Santi TASENA [2]


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.
Bernstein estimator, copula, empirical, Sobolev convergence
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Primary Language en
Subjects Statistics and Probability
Journal Section Statistics
Authors

Orcid: 0000-0002-5864-2685
Author: Sundusit SAEKAOW
Institution: Chiang Mai University
Country: Thailand


Orcid: 0000-0002-7590-5993
Author: Santi TASENA (Primary Author)
Institution: Chiang Mai University
Country: Thailand


Dates

Publication Date : December 8, 2019

Bibtex @research article { hujms464636, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1845 - 1858}, doi = {10.15672/hujms.464636}, title = {Sobolev Convergence of Empirical Bernstein Copulas}, key = {cite}, author = {SAEKAOW, Sundusit and TASENA, Santi} }
APA SAEKAOW, S , TASENA, S . (2019). Sobolev Convergence of Empirical Bernstein Copulas. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1845-1858 . DOI: 10.15672/hujms.464636
MLA SAEKAOW, S , TASENA, S . "Sobolev Convergence of Empirical Bernstein Copulas". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1845-1858 <https://dergipark.org.tr/en/pub/hujms/issue/50516/464636>
Chicago SAEKAOW, S , TASENA, S . "Sobolev Convergence of Empirical Bernstein Copulas". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1845-1858
RIS TY - JOUR T1 - Sobolev Convergence of Empirical Bernstein Copulas AU - Sundusit SAEKAOW , Santi TASENA Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.464636 DO - 10.15672/hujms.464636 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1845 EP - 1858 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.464636 UR - https://doi.org/10.15672/hujms.464636 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Sobolev Convergence of Empirical Bernstein Copulas %A Sundusit SAEKAOW , Santi TASENA %T Sobolev Convergence of Empirical Bernstein Copulas %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/hujms.464636 %U 10.15672/hujms.464636
ISNAD SAEKAOW, Sundusit , TASENA, Santi . "Sobolev Convergence of Empirical Bernstein Copulas". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1845-1858 . https://doi.org/10.15672/hujms.464636
AMA SAEKAOW S , TASENA S . Sobolev Convergence of Empirical Bernstein Copulas. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1845-1858.
Vancouver SAEKAOW S , TASENA S . Sobolev Convergence of Empirical Bernstein Copulas. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1858-1845.