Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation
The empirical multilinear or checkerboard copula process is a promising tool for statistical inference in copula models for data with ties (Genest et al., 2019a). The large-sample behavior of this process was determined in Genest et al. (2014, 2017) under very broad conditions. The purpose of this n...
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Elsevier
2025-06-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X25000035 |
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| author | Christian Genest Johanna G. Nešlehová |
| author_facet | Christian Genest Johanna G. Nešlehová |
| author_sort | Christian Genest |
| collection | DOAJ |
| description | The empirical multilinear or checkerboard copula process is a promising tool for statistical inference in copula models for data with ties (Genest et al., 2019a). The large-sample behavior of this process was determined in Genest et al. (2014, 2017) under very broad conditions. The purpose of this note is to provide a detailed description of this asymptotic result and to derive an expression for the limit of the process in the simplest possible case in which the data form a random sample of pairs of Bernoulli random variables. Although one would never actually fit a copula model to a 2 × 2 contingency table, this case is particularly well suited for explicit calculations and didactic explanations of the intricacies of the limiting behavior of this process and make it clear why the conditions in Genest et al. (2014, 2017) are needed and cannot be simplified. |
| format | Article |
| id | doaj-art-bbbd75ff486448019274f89e1f21fdf3 |
| institution | Kabale University |
| issn | 2666-657X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-bbbd75ff486448019274f89e1f21fdf32025-02-07T04:48:24ZengElsevierExamples and Counterexamples2666-657X2025-06-017100176Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentationChristian Genest0Johanna G. Nešlehová1Corresponding author.; Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal, QC, Canada H3A 0B9,Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal, QC, Canada H3A 0B9,The empirical multilinear or checkerboard copula process is a promising tool for statistical inference in copula models for data with ties (Genest et al., 2019a). The large-sample behavior of this process was determined in Genest et al. (2014, 2017) under very broad conditions. The purpose of this note is to provide a detailed description of this asymptotic result and to derive an expression for the limit of the process in the simplest possible case in which the data form a random sample of pairs of Bernoulli random variables. Although one would never actually fit a copula model to a 2 × 2 contingency table, this case is particularly well suited for explicit calculations and didactic explanations of the intricacies of the limiting behavior of this process and make it clear why the conditions in Genest et al. (2014, 2017) are needed and cannot be simplified.http://www.sciencedirect.com/science/article/pii/S2666657X25000035Asymptotic distributionCheckerboard copulaMultilinear extensionRank-based inferenceTies |
| spellingShingle | Christian Genest Johanna G. Nešlehová Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation Examples and Counterexamples Asymptotic distribution Checkerboard copula Multilinear extension Rank-based inference Ties |
| title | Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation |
| title_full | Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation |
| title_fullStr | Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation |
| title_full_unstemmed | Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation |
| title_short | Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation |
| title_sort | asymptotic behavior of the empirical checkerboard copula process for binary data an educational presentation |
| topic | Asymptotic distribution Checkerboard copula Multilinear extension Rank-based inference Ties |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X25000035 |
| work_keys_str_mv | AT christiangenest asymptoticbehavioroftheempiricalcheckerboardcopulaprocessforbinarydataaneducationalpresentation AT johannagneslehova asymptoticbehavioroftheempiricalcheckerboardcopulaprocessforbinarydataaneducationalpresentation |