Add extensible copula hypothesis testing framework

Project.toml

@@ -21,6 +21,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
 TaylorSeries = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
@@ -60,6 +61,7 @@ Roots = "1, 2, 3"
 SpecialFunctions = "2"
 StableRNGs = "1"
 Statistics = "1"
+StatsAPI = "1.8.0"
 StatsBase = "0.33, 0.34"
 StatsFuns = "0.9, 1.3, 2"
 TaylorSeries = "0.20, 0.21, 0.22"

docs/make.jl

@@ -27,6 +27,7 @@ makedocs(;
             "Conditioning and subsetting"=>"manual/conditioning_and_subsetting.md",
             "Dependence metrics"=>"manual/dependence_measures.md",
             "Fitting"=>"manual/fitting_interface.md",
+            "Hypothesis testing" => "manual/hypothesis_testing.md",
             "Visualizations"=>"manual/visualizations.md",
         ],
         "Bestiary" => [

docs/src/assets/references.bib

@@ -1064,4 +1064,124 @@ @article{gudendorf2012multivariate
   year={2012},
   publisher={Elsevier},
   doi={10.1016/j.jspi.2012.05.007}
-}
+}
+
+@article{genest2004independence,
+  title = {Test of Independence and Randomness Based on the Empirical Copula Process},
+  author = {Genest, Christian and Rémillard, Bruno},
+  year = {2004},
+  journal = {TEST},
+  volume = {13},
+  number = {2},
+  pages = {335--369},
+  doi = {10.1007/BF02595777},
+  keywords = {copula, empirical copula process, independence, Cramer-von Mises}
+}
+
+@article{fermanian2004empirical,
+  title = {Weak Convergence of Empirical Copula Processes},
+  author = {Fermanian, Jean-David and Radulović, Dragan and Wegkamp, Marten},
+  year = {2004},
+  journal = {Bernoulli},
+  volume = {10},
+  number = {5},
+  pages = {847--860},
+  doi = {10.3150/bj/1099579158},
+  keywords = {copula, empirical process, weak convergence}
+}
+
+@article{genest2012symmetry,
+  title = {Tests of Symmetry for Bivariate Copulas},
+  author = {Genest, Christian and Nešlehová, Johanna and Quessy, Jean-François},
+  year = {2012},
+  journal = {Annals of the Institute of Statistical Mathematics},
+  volume = {64},
+  number = {4},
+  pages = {811--834},
+  doi = {10.1007/s10463-011-0337-6},
+  keywords = {copula, symmetry, exchangeability, empirical copula process}
+}
+
+@article{harder2017exchangeability,
+  title = {Testing Exchangeability of Copulas in Arbitrary Dimension},
+  author = {Harder, Michael and Stadtm{"u}ller, Ulrich},
+  year = {2017},
+  journal = {Journal of Nonparametric Statistics},
+  volume = {29},
+  number = {1},
+  pages = {40--60},
+  doi = {10.1080/10485252.2016.1253841},
+  keywords = {copula, exchangeability, multiplier bootstrap, empirical copula}
+}
+
+@article{beare2020symmetry,
+  title = {Randomization Tests of Copula Symmetry},
+  author = {Beare, Brendan K. and Seo, Juwon},
+  year = {2020},
+  journal = {Econometric Theory},
+  volume = {36},
+  number = {6},
+  pages = {1025--1063},
+  doi = {10.1017/S0266466619000410},
+  keywords = {copula, radial symmetry, exchangeability, randomization test}
+}
+
+@article{kojadinovic2011extremevalue,
+  title = {Large-Sample Tests of Extreme-Value Dependence for Multivariate Copulas},
+  author = {Kojadinovic, Ivan and Segers, Johan and Yan, Jun},
+  year = {2011},
+  journal = {Canadian Journal of Statistics},
+  volume = {39},
+  number = {4},
+  pages = {703--720},
+  doi = {10.1002/cjs.10110},
+  keywords = {copula, extreme value, max-stability, multiplier bootstrap}
+}
+
+@article{remillard2009equality,
+  title = {Testing for Equality Between Two Copulas},
+  author = {Rémillard, Bruno and Scaillet, Olivier},
+  year = {2009},
+  journal = {Journal of Multivariate Analysis},
+  volume = {100},
+  number = {3},
+  pages = {377--386},
+  doi = {10.1016/j.jmva.2008.05.004},
+  keywords = {copula, empirical process, multiplier bootstrap, Cramer-von Mises}
+}
+
+@article{bucher2010bootstrap,
+  title = {A Note on Bootstrap Approximations for the Empirical Copula Process},
+  author = {Bücher, Axel and Dette, Holger},
+  year = {2010},
+  journal = {Statistics \& Probability Letters},
+  volume = {80},
+  number = {23--24},
+  pages = {1925--1932},
+  doi = {10.1016/j.spl.2010.08.021},
+  keywords = {copula, empirical process, multiplier bootstrap}
+}
+
+@article{genest2008bootstrap,
+  title = {Validity of the Parametric Bootstrap for Goodness-of-Fit Testing in Semiparametric Models},
+  author = {Genest, Christian and Rémillard, Bruno},
+  year = {2008},
+  journal = {Annales de l'Institut Henri Poincaré, Probabilités et Statistiques},
+  volume = {44},
+  number = {6},
+  pages = {1096--1127},
+  doi = {10.1214/07-AIHP148},
+  keywords = {bootstrap, goodness of fit, copula, semiparametric model}
+}
+
+@article{genest2009gof,
+  title = {Goodness-of-Fit Tests for Copulas: A Review and a Power Study},
+  author = {Genest, Christian and Rémillard, Bruno and Beaudoin, David},
+  year = {2009},
+  journal = {Insurance: Mathematics and Economics},
+  volume = {44},
+  number = {2},
+  pages = {199--213},
+  doi = {10.1016/j.insmatheco.2007.10.005},
+  keywords = {copula, goodness of fit, parametric bootstrap, Cramer-von Mises}
+}