Further contributions to some inequalities for normal distributions and their applications to simultaneous confidence bounds

1970 ◽  
Vol 22 (1) ◽  
pp. 451-458 ◽  
Author(s):  
C. G. Khatri
Keyword(s):  
Confidence Bounds ◽  
Normal Distributions ◽  
Simultaneous Confidence Bounds

SIMULTANEOUS CONFIDENCE BOUNDS FOR LOW-DOSE RISK ASSESSMENT WITH NONQUANTAL DATA

2004 ◽  
Vol 15 (1) ◽  
pp. 17-31 ◽  
Author(s):  
Walter W. Piegorsch ◽  
R. Webster West ◽  
Wei Pan ◽  
Ralph L. Kodell
Keyword(s):  
Risk Assessment ◽  
Low Dose ◽  
Confidence Bounds ◽  
Simultaneous Confidence Bounds ◽  
Nonquantal Data

scholarly journals Corrections: Simultaneous Confidence Bounds

1982 ◽  
Vol 10 (1) ◽  
pp. 321-321 ◽  
Author(s):  
Charles H. Alexander
Keyword(s):  
Confidence Bounds ◽  
Simultaneous Confidence Bounds

scholarly journals Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 841-856 ◽  
Author(s):  
Jelle J Goeman ◽  
Rosa J Meijer ◽  
Thijmen J P Krebs ◽  
Aldo Solari
Keyword(s):  
Large Scale ◽  
Average Power ◽  
Multiple Hypothesis Testing ◽  
Familywise Error Rate ◽  
Confidence Bounds ◽  
Testing Procedures ◽  
False Discovery ◽  
Simultaneous Control ◽  
Simultaneous Confidence Bounds ◽  
False Discovery Proportion

Summary Closed testing procedures are classically used for familywise error rate control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion in all subsets of the hypotheses, allowing for inference robust to post hoc selection of subsets. In this paper we investigate the special case of closed testing with Simes local tests. We construct a novel fast and exact shortcut and use it to investigate the power of this approach when the number of hypotheses goes to infinity. We show that if a minimal level of signal is present, the average power to detect false hypotheses at any desired false discovery proportion does not vanish. Additionally, we show that the confidence bounds for false discovery proportion are consistent estimators for the true false discovery proportion for every nonvanishing subset. We also show close connections between Simes-based closed testing and the procedure of Benjamini and Hochberg.

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