Direction-Projection-Permutation for High-Dimensional Hypothesis Tests

Journal of Computational and Graphical Statistics

Volumn 25, Issue 2, 2016, Pages 549-569

  Wei, Susan ^a   Lee, Chihoon ^a,b   Wichers, Lindsay ^c,d   Marron, J S ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b Veterinary Dentistry and Oral Surgery   (United States)

^c University of North Carolina at Chapel Hill   (United States)

^d U S ENVIRONMENTAL PROTECTION AGENCY   (United States)

Author keywords

Distance weighted discrimination; High dimensional hypothesis test; High dimensional low sample size; Linear binary classification; Permutation test; Two sample problem

Indexed keywords

EID: 84971389584     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2015.1027773     Document Type: Article

References (25)

1. Z.Bai,, H.Saranadasa, (1996), Effect of High Dimension: By an Example of a Two Sample Problem, Statistica Sinica, 6, 311–329.
2. L.Baringhaus,, C.Franz, (2004), On a New Multivariate Two-Sample Test, Journal of Multivariate Analysis, 88, 190–206.
3. L.Baringhaus, (2010), Rigid Motion Invariant Two-Sample Tests, Statistica Sinica, 20, 1333–1361.
4. P.J.Bickel,, L.Breiman, (1983), Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test, The Annals of Probability, 11, 185–214.
5. M.Biswas,, A.K.Ghosh, (2014), A Nonparametric Two-Sample Test Applicable to High Dimensional Data, Journal of Multivariate Analysis, 123, 160–171.
6. T.Cai,, W.Liu,, Y.Xia, (2013), Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings, Journal of the American Statistical Association, 108, 265–277.
7. T.Cai, (2014), Two-Sample Test of High Dimensional Means Under Dependence, Journal of the Royal Statistical Society, Series B, 76, 349–372.
8. L.A.Carey,, C.M.Perou,, C.A.Livasy,, L.G.Dressler,, D.Cowan,, K.Conway,, G.Karaca,, M.A.Troester,, C.K.Tse,, S.D.S.L.G.J.C.M.C.N.T.O.M.P.G.E.H.S.A.M.R.C.Edmiston, S., Deming, S. L., Geradts, J., Cheang, M. C., Nielsen, T. O., Moorman, P. G., Earp, H. S., and Millikan, R. C. (2006), Race, Breast Cancer Subtypes, and Survival in the Carolina Breast Cancer Study, The Journal of the American Medical Association, 295, 2492–2502.
9. S.X.Chen,, Y.-L.Qin, (2010), A Two-Sample Test for High-Dimensional Data With Applications to Gene-Set Testing, The Annals of Statistics, 38, 808–835.
10. E.Y.Chung,, J.P.Romano, (2013), Exact and Asymptotically Robust Permutation Tests, Annals of Statistics, 41, 484--507.
11. M.D.Ernst, (2004), Permutation Methods: A Basis for Exact Inference, Statistical Science, 19, 676–685.
12. J.H.Friedman,, L.C.Rafsky, (1979), Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests, The Annals of Statistics, 7, 697–717.
13. A.K.Ghosh,, M.Biswas, (2013), Exact Distribution-Free Two-Sample Tests Applicable to High Dimensional Data, unpublished manuscript.
14. P.Hall,, J.S.Marron,, A.Neeman, (2005), Geometric Representation of High Dimension, Low Sample Size Data, Journal of the Royal Statistical Society, Series B, 67, 427–444.
15. P.Hall,, N.Tajvidi, (2002), Permutation Tests for Equality of Distributions in High-Dimensional Settings, Biometrika, 89, 359–374.
16. T.Hastie,, R.Tibshirani,, and J.Friedman, (2001), The Elements of Statistical Learning, New York: Springer-Verlag.
17. N.Henze, (1988), A Multivariate Two-Sample Test Based on the Number of Nearest Neighbor Type Coincidences, The Annals of Statistics, 16, 772–783.
18. Y.Huang,, H.Xu,, V.Calian,, J.C.Hsu, (2006), To Permute or Not to Permute, Bioinformatics, 22, 2244–2248.
19. S.Jung,, J.Marron, (2009), PCA Consistency in High Dimension, Low Sample Size Context, The Annals of Statistics, 37, 4104–4130.
20. M.Lopes,, L.Jacob,, M.J.Wainwright, (2011), A More Powerful Two-Sample Test in High Dimensions Using Random Projection, in Advances in Neural Information Processing Systems, eds. M. Lopes, L. Jacob, and M. Wainwright,. 1206–1214.
21. J.Marron,, M.J.Todd,, J.Ahn, (2007), Distance-Weighted Discrimination, Journal of the American Statistical Association, 102, 1267–1271.
22. M.F.Schilling, (1986), Multivariate Two-Sample Tests Based on Nearest Neighbors, Journal of the American Statistical Association, 81, 799–806.
23. M.S.Srivastava,, M.Du, (2008), A Test for the Mean Vector With Fewer Observations Than the Dimension, Journal of Multivariate Analysis, 99, 386–402.
24. G.J.Szekely,, M.L.Rizzo, (2004), Testing for Equal Distributions in High Dimension, InterStat, 5.
25. B.L.Welch, (1947), The Generalization of ‘Student’s’ Problem When Several Different Population Variances are Involved, Biometrika, 34, 28–35.