Bickel (1969) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
9 |
0 |
9 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
Biau and Gyorfi (2005) |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
9 |
0 |
9 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
Boeckel, Spokoiny and Suvorikova (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
Ntoutsi et al. (2008) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
-- |
-- |
11 |
0 |
6 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Ganti et al. (1999) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
11 |
0 |
4 |
6 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Roederer et al. (2001) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✖ |
NA |
-- |
-- |
8 |
0 |
9 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Wang and Pei (2005) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
-- |
-- |
9 |
0 |
8 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Ahmad and Cerrito (1993) |
✖ |
✔ |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
NA |
NA |
NA |
7 |
1 |
8 |
5 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Anderson, Hall and Titterington (1994) |
✖ |
✔ |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
9 |
1 |
8 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Cao and van Keilegom (2006) |
✖ |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
NA |
NA |
5 |
0 |
9 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
Alba-Fernández, Ibáñez-Pérez and Jiménez-Gamero (2004) |
✖ |
✔ |
NA |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
7 |
0 |
8 |
6 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
Alba Fernández, Jiménez Gamero and Muñoz García (2008) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✖ |
✖ |
(✔) |
✔ |
NA |
✔ |
NA |
9 |
1 |
7 |
4 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
Liu, Xia and Zhou (2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
✖ |
✖ |
✖ |
NA |
✔ |
NA |
NA |
NA |
5 |
0 |
9 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
Li, Hu and Zhang (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
NA |
✔ |
NA |
10 |
0 |
4 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
Ghosh and Biswas (2016) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
8 |
0 |
7 |
6 |
Rank-based |
Rank-based |
NA |
Ghosal and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
5 |
9 |
Rank-based |
Rank-based |
R package testOTM |
Deb, Bhattacharya and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Rank-based |
Rank-based |
NA |
Zhou and Chen (2023) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
7 |
3 |
6 |
5 |
Rank-based |
Rank-based |
NA |
Engineer metric (Rachev, 1991) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✖ |
✔ |
✔ |
-- |
-- |
8 |
0 |
10 |
1 |
Discrepancy measure for distributions |
Probability metric |
NA |
Zolotarev's (semi)metric (Rachev, 1991) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
✖ |
(✔) |
✔ |
✔ |
-- |
-- |
5 |
3 |
6 |
5 |
Discrepancy measure for distributions |
Probability metric |
NA |
Ky Fan metric (Rachev, 1991) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
(✔) |
(✔) |
✖ |
✔ |
✔ |
✔ |
-- |
-- |
8 |
2 |
5 |
4 |
Discrepancy measure for distributions |
Probability metric |
NA |
Prokhorov metric (Rachev, 1991) |
✖ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
7 |
0 |
5 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
Dudley metric |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
9 |
0 |
3 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
Total variation metric (Zolotarev, 1984) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
9 |
0 |
3 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
Kantorovich-Rubinstein metric (Zolotarev, 1984, Dudley, 1989) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
8 |
0 |
3 |
8 |
Discrepancy measure for distributions |
Probability metric |
NA |
metric |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
7 |
0 |
4 |
8 |
Discrepancy measure for distributions |
Probability metric |
NA |
q-Wasserstein metrics |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
✖ |
✔ |
✔ |
✔ |
-- |
-- |
9 |
2 |
7 |
1 |
Discrepancy measure for distributions |
Probability metric |
R package approxOT, transport |
(Squared) Hellinger distance |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
9 |
1 |
3 |
6 |
Discrepancy measure for distributions |
Divergence |
R package abdiv |
Vincze Le Cam distance (Vincze, 1981, Le Cam, 1986) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
8 |
1 |
3 |
7 |
Discrepancy measure for distributions |
Divergence |
NA |
KL divergence (Kullback and Leibler, 1951) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✖ |
✖ |
-- |
-- |
10 |
0 |
6 |
3 |
Discrepancy measure for distributions |
Divergence |
R package FNN |
Jeffrey's divergence |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✖ |
-- |
-- |
11 |
0 |
5 |
3 |
Discrepancy measure for distributions |
Divergence |
R package FNN |
Extended divergence |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
8 |
1 |
4 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
Jensen Shannon divergence |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
-- |
-- |
10 |
1 |
3 |
5 |
Discrepancy measure for distributions |
Divergence |
R package philentropy |
Pearson divergence (Pearson, 1900) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✖ |
✖ |
-- |
-- |
9 |
0 |
6 |
4 |
Discrepancy measure for distributions |
Divergence |
NA |
Relative Pearson divergence (Yamada et al., 2013) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✖ |
✖ |
-- |
-- |
7 |
0 |
6 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
f-dissimilarity (García-García and Williamson, 2012, Györfi and Nemetz, 1975) |
✖ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
NA |
-- |
-- |
10 |
1 |
3 |
5 |
Discrepancy measure for distributions |
Divergence |
NA |
Rényi divergence (Rényi, 1961) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
NA |
NA |
NA |
(✔) |
✖ |
✖ |
-- |
-- |
4 |
1 |
7 |
7 |
Discrepancy measure for distributions |
Divergence |
NA |
Relative information of type s (Taneja and Kumar, 2004) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✖ |
NA |
-- |
-- |
4 |
0 |
6 |
9 |
Discrepancy measure for distributions |
Divergence |
NA |
H-divergence (Zhao et al., 2021) |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
(✔) |
(✔) |
NA |
NA |
NA |
6 |
2 |
5 |
8 |
Discrepancy measure for distributions |
Divergence |
NA |
Muñoz et al. (2012) |
✖ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
6 |
0 |
7 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
Muñoz, Martos and González (2013) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
7 |
0 |
7 |
5 |
Discrepancy measure for distributions |
Divergence |
NA |
Friedman and Rafsky (1979) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
✖ |
14 |
0 |
6 |
1 |
Graph-based |
Graph-based |
R package gTests |
Rosenbaum (2005) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
NA |
14 |
0 |
5 |
2 |
Graph-based |
Graph-based |
R package crossmatch |
Chen and Zhang (2013) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✔ |
✔ |
✔ |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
9 |
0 |
6 |
3 |
Graph-based |
Graph-based |
R packages gTests, gCat |
Biswas, Mukhopadhyay and Ghosh (2014) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
✔ |
13 |
0 |
5 |
3 |
Graph-based |
Graph-based |
R package LPKsample |
Petrie (2016) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
13 |
0 |
4 |
4 |
Graph-based |
Graph-based |
R package multicross |
Chen and Friedman (2017) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
12 |
0 |
5 |
4 |
Graph-based |
Graph-based |
R package gTests |
Chen, Chen and Su (2018) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
13 |
0 |
5 |
3 |
Graph-based |
Graph-based |
NA |
Zhang and Chen (2019) (weighted) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
9 |
0 |
6 |
3 |
Graph-based |
Graph-based |
R package gTests |
Zhang and Chen (2019) (generalized) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
8 |
0 |
6 |
4 |
Graph-based |
Graph-based |
R package gTests |
Zhang and Chen (2019) (max-type) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
NA |
NA |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
7 |
0 |
6 |
5 |
Graph-based |
Graph-based |
R package gTests |
Sarkar, Biswas and Ghosh (2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
(✔) |
✔ |
NA |
NA |
✔ |
NA |
NA |
✔ |
9 |
1 |
6 |
5 |
Graph-based |
Graph-based |
NA |
Mukhopadhyay and Wang (2020) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
9 |
0 |
4 |
8 |
Graph-based |
Graph-based |
R package LPKsample |
Mukherjee et al. (2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
14 |
0 |
3 |
4 |
Graph-based |
Graph-based |
R package multicross |
Song and Chen (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
12 |
0 |
5 |
4 |
Graph-based |
Graph-based |
R package gTestsMulti |
Weiss (1960) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
NA |
NA |
NA |
11 |
0 |
5 |
5 |
Graph-based |
Graph-based (NN) |
NA |
Friedman and Steppel (1973) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
|
✖ |
NA |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
NA |
✔ |
NA |
9 |
1 |
5 |
6 |
Graph-based |
Graph-based (NN) |
NA |
Schilling (1986), Henze (1988) |
✖ |
✔ |
✖ |
✔ |
✔ |
(✔) |
✔ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
✖ |
12 |
1 |
6 |
2 |
Graph-based |
Graph-based (NN) |
NA |
Barakat, Quade and Salama (1996) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
NA |
11 |
0 |
6 |
4 |
Graph-based |
Graph-based (NN) |
NA |
Nettleton and Banerjee (2001) |
✖ |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
-- |
NA |
✔ |
NA |
NA |
NA |
10 |
0 |
3 |
5 |
Graph-based |
Graph-based (NN) |
NA |
Hall and Tajvidi (2002) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
10 |
0 |
6 |
5 |
Graph-based |
Graph-based (NN) |
NA |
Chen, Dou and Qiao (2013) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
NA |
11 |
0 |
7 |
3 |
Graph-based |
Graph-based (NN) |
NA |
Mondal, Biswas and Ghosh (2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
(✔) |
11 |
1 |
6 |
3 |
Graph-based |
Graph-based (NN) |
NA |
Energy statistic (Zech and Aslan, 2003) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
(✔) |
14 |
1 |
6 |
0 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package energy |
Generalized energy statistic (Sejdinovic et al., 2013) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
(✔) |
✔ |
(✔) |
✔ |
NA |
10 |
2 |
7 |
2 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Chakraborty and Zhang (2021) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
(✔) |
✔ |
(✔) |
11 |
2 |
7 |
1 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
DISCO (Rizzo and Székely, 2010) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
✔ |
NA |
✔ |
NA |
11 |
0 |
7 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package energy |
Huang and Huo (2017) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
NA |
NA |
7 |
0 |
10 |
4 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Deb and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
|
✖ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
13 |
0 |
4 |
4 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R code on GitHub |
Al-Labadi, Asl and Saberi (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
NA |
10 |
0 |
5 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Baringhaus and Franz (2010) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
12 |
0 |
6 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package cramer |
Liu and Modarres (2011) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
(✔) |
NA |
NA |
NA |
9 |
1 |
5 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Biswas and Ghosh (2014) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
✔ |
13 |
0 |
5 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Sarkar and Ghosh (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
NA |
✔ |
9 |
0 |
6 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Montero-Manso and Vilar (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
NA |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
NA |
9 |
0 |
5 |
7 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
Tsukada (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
✔ |
11 |
0 |
5 |
5 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
MMD (Muandet et al., 2017, Gretton et al., 2009, , Gretton et al., 2012) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
✔ |
(✔) |
NA |
9 |
5 |
5 |
2 |
Kernel-based |
Kernel-based (MMD) |
NA |
Block MMD (Zaremba et al., 2013) |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
✔ |
NA |
NA |
8 |
4 |
6 |
3 |
Kernel-based |
Kernel-based (MMD) |
matlab code on GitHub |
fastMMD (Zhao and Meng, 2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
(✔) |
✔ |
(✔) |
✔ |
✔ |
✔ |
NA |
NA |
9 |
2 |
6 |
4 |
Kernel-based |
Kernel-based (MMD) |
NA |
ME (Chwialkowski et al., 2015, Jitkrittum et al., 2016) |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
NA |
NA |
NA |
6 |
3 |
7 |
5 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
SCF (Chwialkowski et al., 2015, Jitkrittum et al., 2016) |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
5 |
3 |
7 |
6 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
regularized MMD (Danafar et al., 2014) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
|
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
7 |
4 |
4 |
6 |
Kernel-based |
Kernel-based (MMD) |
NA |
Anisotropic kernel MMD (Cheng, Cloninger and Coifman, 2020) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
(✔) |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✔ |
NA |
✔ |
NA |
5 |
1 |
8 |
7 |
Kernel-based |
Kernel-based (MMD) |
NA |
DMMD/ DFDA (Kirchler et al., 2020) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
8 |
3 |
6 |
4 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
GPK (Song and Chen, 2023) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
8 |
3 |
5 |
5 |
Kernel-based |
Kernel-based (MMD) |
R package kerTests |
Kernel FDA (Moulines, Bach and Harchaoui, 2007) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
(✔) |
NA |
✔ |
NA |
5 |
2 |
5 |
9 |
Kernel-based |
Kernel-based |
NA |
Fromont et al. (2012) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
5 |
0 |
6 |
10 |
Kernel-based |
Kernel-based |
NA |
Scetbon and Varoquaux (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
(✔) |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
6 |
4 |
7 |
4 |
Kernel-based |
Kernel-based |
NA |
Kernel-based quadratic distance (Chen and Markatou, 2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
7 |
3 |
5 |
6 |
Kernel-based |
Kernel-based |
NA |
Bayesian kernel test (Zhang et al., 2022) |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
NA |
✔ |
NA |
NA |
NA |
7 |
1 |
7 |
6 |
Kernel-based |
Kernel-based |
NA |
KMD (Huang & Sen, 2023) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
|
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
16 |
0 |
3 |
2 |
Kernel-based |
Kernel-based |
R package KMD |
Friedman (2004) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
(✔) |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
3 |
6 |
5 |
7 |
Method based on binary classification |
Method based on binary classification |
NA |
C2ST (Lopez-Paz and Oquab, 2017) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
(✔) |
NA |
7 |
6 |
5 |
3 |
Method based on binary classification |
Method based on binary classification |
R package Ecume |
Regression based test (Kim, Lee and Lei, 2019) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
NA |
NA |
5 |
5 |
6 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
Cheng and Cloninger (2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
5 |
3 |
8 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
Yu et al. (2007) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
11 |
0 |
5 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
DiProPerm test (Wei et al., 2016) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
(✔) |
NA |
5 |
5 |
6 |
5 |
Method based on binary classification |
Method based on binary classification |
R package diproperm |
Classifier Probability Test (Cai, Goggin and Jiang, 2020) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
NA |
NA |
2 |
5 |
7 |
7 |
Method based on binary classification |
Method based on binary classification |
NA |
Kim et al. (2021) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
(✔) |
(✔) |
6 |
7 |
5 |
3 |
Method based on binary classification |
Method based on binary classification |
NA |
Hediger, Michel and Näf (2021) |
✖ |
✔ |
✔ |
(✔) |
✔ |
✖ |
(✔) |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
(✔) |
NA |
11 |
3 |
4 |
3 |
Method based on binary classification |
Method based on binary classification |
R package hypoRF |
Feurer, Springenberg and Hutter (2015) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
(✔) |
NA |
NA |
NA |
NA |
✔ |
NA |
-- |
-- |
9 |
1 |
3 |
6 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
Gromov-Hausdoff distance (Mémoli, 2017) |
✖ |
✔ |
(✔) |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
5 |
1 |
5 |
8 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
Leite, Brazdil and Vanschoren (2012), Leite and Brazdil (2021) |
✔ |
✔ |
✔ |
✔ |
(✔) |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
(✔) |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
✖ |
✔ |
✖ |
-- |
-- |
10 |
5 |
3 |
1 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
DeDiMs (Calderon Ramirez et al., 2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✖ |
✖ |
NA |
NA |
6 |
0 |
8 |
7 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
Alvarez-Melis and Fusi (2020) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
NA |
✔ |
✔ |
✔ |
-- |
-- |
11 |
2 |
4 |
2 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
python code on GitHub |
DataSpheres (Johnson and Dasu, 1998) |
✖ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
6 |
0 |
5 |
10 |
Comparison based on summary statistics |
Comparison based on summary statistics |
NA |
Constrained minimum distance (Tatti, 2007) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
8 |
0 |
6 |
5 |
Comparison based on summary statistics |
Comparison based on summary statistics |
NA |
Romano (1989) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
(✔) |
NA |
NA |
✔ |
NA |
✔ |
NA |
10 |
1 |
3 |
7 |
Testing approach |
Testing approach |
NA |
Burke (2000) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
✖ |
✖ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Testing approach |
Testing approach |
NA |
Ping (2000) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
8 |
0 |
5 |
8 |
Testing approach |
Testing approach |
NA |
Chen and Hanson (2014) |
✖ |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
NA |
7 |
0 |
7 |
7 |
Testing approach |
Testing approach |
NA |
Zhou, Zheng and Zhang (2017) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✖ |
NA |
(✔) |
(✔) |
5 |
2 |
8 |
6 |
Testing approach |
Testing approach |
NA |
Pan et al. (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
✔ |
NA |
11 |
0 |
5 |
5 |
Testing approach |
Testing ap |