A combined p-value test for the mean difference of high-dimensional data
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摘要
This paper proposes a novel method for testing the equality of high-dimensional means using a multiple hypothesis test. The proposed method is based on the maximum of standardized partial sums of logarithmic p-values statistic. Numerical studies show that the method performs well for both normal and non-normal data and has a good power performance under both dense and sparse alternative hypotheses. For illustration, a real data analysis is implemented.
This paper proposes a novel method for testing the equality of high-dimensional means using a multiple hypothesis test. The proposed method is based on the maximum of standardized partial sums of logarithmic p-values statistic. Numerical studies show that the method performs well for both normal and non-normal data and has a good power performance under both dense and sparse alternative hypotheses. For illustration, a real data analysis is implemented.
This paper proposes a novel method for testing the equality of high-dimensional means using a multiple hypothesis test. The proposed method is based on the maximum of standardized partial sums of logarithmic p-values statistic. Numerical studies show that the method performs well for both normal and non-normal data and has a good power performance under both dense and sparse alternative hypotheses. For illustration, a real data analysis is implemented.
引文
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2 Bennett B M.Note on a solution of the generalized Behrens-Fisher problem.Ann Inst Statist Math,1951,2:87-90
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5 Cai T,Liu W D,Xia Y.Two-sample test of high dimensional means under dependency.J R Stat Soc Ser B Stat Methodol,2014,76:349-372
6 Chakraborty A K,Chatterjee M.On multivariate folded normal distribution.Sankhyˉa,2013,75:1-15
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8 David H A,Nagaraja H N.Order Statistics,3rd ed.Hoboken:John Wiley&Sons,2003
9 Dong Z C,Yu W,Xu W L.A modified combined p-value multiple test.J Stat Comput Simul,2015,85:2479-2490
10 Dudbridge F,Koeleman B P C.Rank truncated product of P values,with application to genomewide association scans.Genet Epidemiol,2003,25:360-366
11 Feng L,Zou C L,Wang Z J,et al.Two-sample Behrens-Fisher problem for high-dimensional data.Statist Sinica,2015,25:1297-1312
12 Fisher R A.Statistical Methods for Research Workers.London:Oliver and Boyd,1932
13 Gregory K B,Carroll R J,Baladandayuthapani V,et al.A two-sample test for equality of means in high dimension.J Amer Statist Assoc,2015,110:837-849
14 Gupta A K,Nadarajah S.Handbook of Beta Distribution and Its Applications.New York:Marcel Dekker,2004
15 Hall P,Jing B-Y,Lahiri S N.On the sampling window method for long-range dependent data.Statist Sinica,1998,8:1189-1204
16 Hu X J,Gadbury G L,Xiang Q F,et al.Illustrations on using the distribution of a P-value in high-dimensional data analyses.Adv Appl Stat Sci,2010,1:191-213
17 Sheng X,Yang J.An adaptive truncated product method for combining dependent p-values.Economics Letters,2013,119:180-182
18 Srivastava M.Multivariate theory for analyzing high dimensional data.J Japan Statist Soc,2007,37:53-86
19 Tsanas A,Little M A,Fox C,et al.Objective automatic assessment of rehabilitative speech treatment in Parkinson’s disease.IEEE Trans Neural Syst Rehabil Eng,2014,22:181-190
20 Yu K,Li Q,Bergen W A,et al.Pathway analysis by adaptive combination of P-values.Genet Epidemiol,2009,22:170-185
21 Zaykin D V,Zhivotovsky L A,Westfall P H,et al.Truncated product method for combining P-values.Genet Epidemiol,2002,22:170-185
22 Zhang S,Chen H,Pfeiffer R M.A combined p-value test for multiple hypothesis testing.J Statist Plann Inference,2013,143:764-770
2 Bennett B M.Note on a solution of the generalized Behrens-Fisher problem.Ann Inst Statist Math,1951,2:87-90
3 Cai T,Liu W D.Adaptive thresholding for sparse covariance matrix estimation.J Amer Statist Assoc,2011,106:672-684
4 Cai T,Liu W D,Luo X.A constrained l1 minimization approach to sparse precision matrix estimation.J Amer Statist Assoc,2011,106:594-607
5 Cai T,Liu W D,Xia Y.Two-sample test of high dimensional means under dependency.J R Stat Soc Ser B Stat Methodol,2014,76:349-372
6 Chakraborty A K,Chatterjee M.On multivariate folded normal distribution.Sankhyˉa,2013,75:1-15
7 Chen S X,Qin Y L.A two-sample test for high-dimensional data with applications to gene-set testing.Ann Statist,2010,38:808-835
8 David H A,Nagaraja H N.Order Statistics,3rd ed.Hoboken:John Wiley&Sons,2003
9 Dong Z C,Yu W,Xu W L.A modified combined p-value multiple test.J Stat Comput Simul,2015,85:2479-2490
10 Dudbridge F,Koeleman B P C.Rank truncated product of P values,with application to genomewide association scans.Genet Epidemiol,2003,25:360-366
11 Feng L,Zou C L,Wang Z J,et al.Two-sample Behrens-Fisher problem for high-dimensional data.Statist Sinica,2015,25:1297-1312
12 Fisher R A.Statistical Methods for Research Workers.London:Oliver and Boyd,1932
13 Gregory K B,Carroll R J,Baladandayuthapani V,et al.A two-sample test for equality of means in high dimension.J Amer Statist Assoc,2015,110:837-849
14 Gupta A K,Nadarajah S.Handbook of Beta Distribution and Its Applications.New York:Marcel Dekker,2004
15 Hall P,Jing B-Y,Lahiri S N.On the sampling window method for long-range dependent data.Statist Sinica,1998,8:1189-1204
16 Hu X J,Gadbury G L,Xiang Q F,et al.Illustrations on using the distribution of a P-value in high-dimensional data analyses.Adv Appl Stat Sci,2010,1:191-213
17 Sheng X,Yang J.An adaptive truncated product method for combining dependent p-values.Economics Letters,2013,119:180-182
18 Srivastava M.Multivariate theory for analyzing high dimensional data.J Japan Statist Soc,2007,37:53-86
19 Tsanas A,Little M A,Fox C,et al.Objective automatic assessment of rehabilitative speech treatment in Parkinson’s disease.IEEE Trans Neural Syst Rehabil Eng,2014,22:181-190
20 Yu K,Li Q,Bergen W A,et al.Pathway analysis by adaptive combination of P-values.Genet Epidemiol,2009,22:170-185
21 Zaykin D V,Zhivotovsky L A,Westfall P H,et al.Truncated product method for combining P-values.Genet Epidemiol,2002,22:170-185
22 Zhang S,Chen H,Pfeiffer R M.A combined p-value test for multiple hypothesis testing.J Statist Plann Inference,2013,143:764-770