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An Approach to the Conditional Error Rate Principle with Nuisance Parameters
Author(s) -
Gutjahr Georg,
Brannath Werner,
Bauer Peter
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01507.x
Subject(s) - nuisance parameter , nuisance , dependency (uml) , mathematics , conditional expectation , word error rate , conditional probability , conditional variance , statistics , mathematical optimization , computer science , econometrics , artificial intelligence , law , volatility (finance) , autoregressive conditional heteroskedasticity , estimator , political science
Summary In the presence of nuisance parameters, the conditional error rate principle is difficult to apply because of the dependency of the conditional error function of the preplanned test on nuisance parameters. To use the conditional error rate principle with nuisance parameters, we propose to search among tests that guarantee overall error control for the test that maximizes a weighted combination of the conditional error rates over possible values of the nuisance parameters. We show that the optimization problem that defines such a test can be solved efficiently by existing algorithms.