TABLE 2 Open in new tab Results for...

Method	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH
Parameters	AR(1), \|$\pi=0.3,\rho=0.8$\|	Banded(1), \|$\pi=0.3,\rho=0.5$\|
mFDR	0.0362	0.0425	0.0377	0.0437	0.0355	0.0420	0.0353	0.0380	0.0422	0.0432	0.0351	0.0415
s.e.(mFDR)	0.0007	0.0003	0.0002	0.0007	0.0007	0.0007	0.0005	0.0004	0.0003	0.0006	0.0005	0.0005
FDR	0.0358	0.0425	0.0377	0.0432	0.0351	0.0415	0.0352	0.0380	0.0422	0.0430	0.0348	0.0413
s.e.(FDR)	0.0007	0.0003	0.0002	0.0007	0.0006	0.0007	0.0005	0.0004	0.0003	0.0005	0.0005	0.0005
TP	241.8	1100.3	1274.4	273.7	242.2	269.6	241.0	532.0	621.7	273.2	241.8	269.6
s.e.(TP)	1.1656	1.6391	2.0912	1.1889	1.1164	1.2358	1.0267	1.3419	1.2943	1.1536	1.1097	1.1918
Parameters	AR(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.8$\|	Banded(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.5$\|
mFDR	0.0461	0.0491	0.0438	0.0542	0.0471	0.0495	0.0457	0.0425	0.0467	0.0549	0.0479	0.0507
s.e.(mFDR)	0.0018	0.0019	0.0018	0.0018	0.0017	0.0019	0.0015	0.0008	0.0007	0.0015	0.0015	0.0015
FDR	0.0435	0.0489	0.0439	0.0516	0.0441	0.0463	0.0451	0.0423	0.0466	0.0538	0.0462	0.0490
s.e.(FDR)	0.0017	0.0019	0.0019	0.0018	0.0017	0.0017	0.0015	0.0007	0.0006	0.0015	0.0015	0.0015
TP	41.3	353.5	394.8	46.5	43.7	45.2	41.5	137.4	188.1	46.3	43.3	44.7
s.e.(TP)	0.4515	1.2378	1.5819	0.4714	0.4880	0.4980	0.3878	0.6367	0.6770	0.4403	0.4561	0.4606

Method

|$\hat{\boldsymbol{T}}_0$|-rule

|$\hat{\boldsymbol{T}}_1$|-rule

|$\hat{\boldsymbol{T}}_2$|-rule

Sun and Cai

ABH

|$\hat{\boldsymbol{T}}_0$|-rule

|$\hat{\boldsymbol{T}}_1$|-rule

|$\hat{\boldsymbol{T}}_2$|-rule

Sun and Cai

ABH

Parameters

AR(1), |$\pi=0.3,\rho=0.8$|

Banded(1), |$\pi=0.3,\rho=0.5$|

mFDR

0.0362

0.0425

0.0377

0.0437

0.0355

0.0420

0.0353

0.0380

0.0422

0.0432

0.0351

0.0415

s.e.(mFDR)

0.0007

0.0003

0.0002

0.0007

0.0005

0.0004

0.0003

0.0006

0.0005

FDR

0.0358

0.0425

0.0377

0.0432

0.0351

0.0415

0.0352

0.0380

0.0422

0.0430

0.0348

0.0413

s.e.(FDR)

0.0007

0.0003

0.0002

0.0007

0.0006

0.0007

0.0005

0.0004

0.0003

0.0005

241.8

1100.3

1274.4

273.7

242.2

269.6

241.0

532.0

621.7

273.2

241.8

269.6

s.e.(TP)

1.1656

1.6391

2.0912

1.1889

1.1164

1.2358

1.0267

1.3419

1.2943

1.1536

1.1097

1.1918

Parameters

AR(1), |$\pi =0.1$|⁠, |$\rho = 0.8$|

Banded(1), |$\pi =0.1$|⁠, |$\rho = 0.5$|

mFDR

0.0461

0.0491

0.0438

0.0542

0.0471

0.0495

0.0457

0.0425

0.0467

0.0549

0.0479

0.0507

s.e.(mFDR)

0.0018

0.0019

0.0018

0.0018

0.0017

0.0019

0.0015

0.0008

0.0007

0.0015

FDR

0.0435

0.0489

0.0439

0.0516

0.0441

0.0463

0.0451

0.0423

0.0466

0.0538

0.0462

0.0490

s.e.(FDR)

0.0017

0.0019

0.0019

0.0018

0.0017

0.0015

0.0007

0.0006

0.0015

41.3

353.5

394.8

46.5

43.7

45.2

41.5

137.4

188.1

46.3

43.3

44.7

s.e.(TP)

0.4515

1.2378

1.5819

0.4714

0.4880

0.4980

0.3878

0.6367

0.6770

0.4403

0.4561

0.4606

Method	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH
Parameters	AR(1), \|$\pi=0.3,\rho=0.8$\|	Banded(1), \|$\pi=0.3,\rho=0.5$\|
mFDR	0.0362	0.0425	0.0377	0.0437	0.0355	0.0420	0.0353	0.0380	0.0422	0.0432	0.0351	0.0415
s.e.(mFDR)	0.0007	0.0003	0.0002	0.0007	0.0007	0.0007	0.0005	0.0004	0.0003	0.0006	0.0005	0.0005
FDR	0.0358	0.0425	0.0377	0.0432	0.0351	0.0415	0.0352	0.0380	0.0422	0.0430	0.0348	0.0413
s.e.(FDR)	0.0007	0.0003	0.0002	0.0007	0.0006	0.0007	0.0005	0.0004	0.0003	0.0005	0.0005	0.0005
TP	241.8	1100.3	1274.4	273.7	242.2	269.6	241.0	532.0	621.7	273.2	241.8	269.6
s.e.(TP)	1.1656	1.6391	2.0912	1.1889	1.1164	1.2358	1.0267	1.3419	1.2943	1.1536	1.1097	1.1918
Parameters	AR(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.8$\|	Banded(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.5$\|
mFDR	0.0461	0.0491	0.0438	0.0542	0.0471	0.0495	0.0457	0.0425	0.0467	0.0549	0.0479	0.0507
s.e.(mFDR)	0.0018	0.0019	0.0018	0.0018	0.0017	0.0019	0.0015	0.0008	0.0007	0.0015	0.0015	0.0015
FDR	0.0435	0.0489	0.0439	0.0516	0.0441	0.0463	0.0451	0.0423	0.0466	0.0538	0.0462	0.0490
s.e.(FDR)	0.0017	0.0019	0.0019	0.0018	0.0017	0.0017	0.0015	0.0007	0.0006	0.0015	0.0015	0.0015
TP	41.3	353.5	394.8	46.5	43.7	45.2	41.5	137.4	188.1	46.3	43.3	44.7
s.e.(TP)	0.4515	1.2378	1.5819	0.4714	0.4880	0.4980	0.3878	0.6367	0.6770	0.4403	0.4561	0.4606

TABLE 2

Open in new tab

Results for different covariance structure (data driven) and different parameters of the model (7). For each multiple testing procedure, we provide the false discovery rate (FDR), marginal false discovery rate (mFDR), and expected true positives (TP) and their standard error. Based on 500 data generations. In bold, the most powerful procedure. |$K=15000,b=0,\tau = \sqrt{2}$|⁠.

Method	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH
Parameters	AR(1), \|$\pi=0.3,\rho=0.8$\|						Banded(1), \|$\pi=0.3,\rho=0.5$\|
mFDR	0.0362	0.0425	0.0377	0.0437	0.0355	0.0420	0.0353	0.0380	0.0422	0.0432	0.0351	0.0415
s.e.(mFDR)	0.0007	0.0003	0.0002	0.0007	0.0007	0.0007	0.0005	0.0004	0.0003	0.0006	0.0005	0.0005
FDR	0.0358	0.0425	0.0377	0.0432	0.0351	0.0415	0.0352	0.0380	0.0422	0.0430	0.0348	0.0413
s.e.(FDR)	0.0007	0.0003	0.0002	0.0007	0.0006	0.0007	0.0005	0.0004	0.0003	0.0005	0.0005	0.0005
TP	241.8	1100.3	1274.4	273.7	242.2	269.6	241.0	532.0	621.7	273.2	241.8	269.6
s.e.(TP)	1.1656	1.6391	2.0912	1.1889	1.1164	1.2358	1.0267	1.3419	1.2943	1.1536	1.1097	1.1918
Parameters	AR(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.8$\|						Banded(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.5$\|
mFDR	0.0461	0.0491	0.0438	0.0542	0.0471	0.0495	0.0457	0.0425	0.0467	0.0549	0.0479	0.0507
s.e.(mFDR)	0.0018	0.0019	0.0018	0.0018	0.0017	0.0019	0.0015	0.0008	0.0007	0.0015	0.0015	0.0015
FDR	0.0435	0.0489	0.0439	0.0516	0.0441	0.0463	0.0451	0.0423	0.0466	0.0538	0.0462	0.0490
s.e.(FDR)	0.0017	0.0019	0.0019	0.0018	0.0017	0.0017	0.0015	0.0007	0.0006	0.0015	0.0015	0.0015
TP	41.3	353.5	394.8	46.5	43.7	45.2	41.5	137.4	188.1	46.3	43.3	44.7
s.e.(TP)	0.4515	1.2378	1.5819	0.4714	0.4880	0.4980	0.3878	0.6367	0.6770	0.4403	0.4561	0.4606

Method	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH	\|$\hat{\boldsymbol{T}}_0$\|-rule	\|$\hat{\boldsymbol{T}}_1$\|-rule	\|$\hat{\boldsymbol{T}}_2$\|-rule	Sun and Cai	BH	ABH
Parameters	AR(1), \|$\pi=0.3,\rho=0.8$\|						Banded(1), \|$\pi=0.3,\rho=0.5$\|
mFDR	0.0362	0.0425	0.0377	0.0437	0.0355	0.0420	0.0353	0.0380	0.0422	0.0432	0.0351	0.0415
s.e.(mFDR)	0.0007	0.0003	0.0002	0.0007	0.0007	0.0007	0.0005	0.0004	0.0003	0.0006	0.0005	0.0005
FDR	0.0358	0.0425	0.0377	0.0432	0.0351	0.0415	0.0352	0.0380	0.0422	0.0430	0.0348	0.0413
s.e.(FDR)	0.0007	0.0003	0.0002	0.0007	0.0006	0.0007	0.0005	0.0004	0.0003	0.0005	0.0005	0.0005
TP	241.8	1100.3	1274.4	273.7	242.2	269.6	241.0	532.0	621.7	273.2	241.8	269.6
s.e.(TP)	1.1656	1.6391	2.0912	1.1889	1.1164	1.2358	1.0267	1.3419	1.2943	1.1536	1.1097	1.1918
Parameters	AR(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.8$\|						Banded(1), \|$\pi =0.1$\|⁠, \|$\rho = 0.5$\|
mFDR	0.0461	0.0491	0.0438	0.0542	0.0471	0.0495	0.0457	0.0425	0.0467	0.0549	0.0479	0.0507
s.e.(mFDR)	0.0018	0.0019	0.0018	0.0018	0.0017	0.0019	0.0015	0.0008	0.0007	0.0015	0.0015	0.0015
FDR	0.0435	0.0489	0.0439	0.0516	0.0441	0.0463	0.0451	0.0423	0.0466	0.0538	0.0462	0.0490
s.e.(FDR)	0.0017	0.0019	0.0019	0.0018	0.0017	0.0017	0.0015	0.0007	0.0006	0.0015	0.0015	0.0015
TP	41.3	353.5	394.8	46.5	43.7	45.2	41.5	137.4	188.1	46.3	43.3	44.7
s.e.(TP)	0.4515	1.2378	1.5819	0.4714	0.4880	0.4980	0.3878	0.6367	0.6770	0.4403	0.4561	0.4606

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