TY - JOUR
T1 - On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence
AU - Chen, Feifei
AU - Meintanis, Simos G.
AU - Zhu, Lixing
N1 - Funding Information:
The authors wish to sincerely thank the Editor-in-Chief, an Associate Editor and anonymous referees for their constructive criticism that led to an improved version of this work. This research was supported by a grant from The University Grants Council of Hong Kong . Chen’s research was supported by the Outstanding Innovative Talents Cultivation Funded Programs 2017 of Renmin University of China . The work of Simos Meintanis was supported by grant number KA: 70/4/7658 of the program ‘Kapodistrias’ of the special account for research grants (EKE) of the National and Kapodistrian University of Athens.
PY - 2019/9
Y1 - 2019/9
N2 - We propose three new characterizations and corresponding distance-based weighted test criteria for the two-sample problem, and for testing symmetry and independence with multivariate data. All quantities have the common feature of involving characteristic functions, and it is seen that these quantities are intimately related to some earlier methods, thereby generalizing them. The connection rests on a special choice of the weight function involved. Equivalent expressions of the distances in terms of densities are given as well as a Bayesian interpretation of the weight function is involved. The asymptotic behavior of the tests is investigated both under the null hypothesis and under alternatives, and affine invariant versions of the test criteria are suggested. Numerical studies are conducted to examine the performances of the criteria. It is shown that the normal weight function, which is the hitherto most often used, is seriously suboptimal. The procedures are biased in the sense that the corresponding test criteria degenerate in high dimension and hence a bias correction is required as the dimension tends to infinity.
AB - We propose three new characterizations and corresponding distance-based weighted test criteria for the two-sample problem, and for testing symmetry and independence with multivariate data. All quantities have the common feature of involving characteristic functions, and it is seen that these quantities are intimately related to some earlier methods, thereby generalizing them. The connection rests on a special choice of the weight function involved. Equivalent expressions of the distances in terms of densities are given as well as a Bayesian interpretation of the weight function is involved. The asymptotic behavior of the tests is investigated both under the null hypothesis and under alternatives, and affine invariant versions of the test criteria are suggested. Numerical studies are conducted to examine the performances of the criteria. It is shown that the normal weight function, which is the hitherto most often used, is seriously suboptimal. The procedures are biased in the sense that the corresponding test criteria degenerate in high dimension and hence a bias correction is required as the dimension tends to infinity.
KW - Characteristic function
KW - Distance correlation
KW - Independence testing
KW - Symmetry testing
KW - Two-sample problem
UR - http://www.scopus.com/inward/record.url?scp=85062440016&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2019.02.006
DO - 10.1016/j.jmva.2019.02.006
M3 - Journal article
AN - SCOPUS:85062440016
SN - 0047-259X
VL - 173
SP - 125
EP - 144
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -