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Full-Text Articles in Physical Sciences and Mathematics
Multiple Testing. Part Ii. Step-Down Procedures For Control Of The Family-Wise Error Rate, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
Multiple Testing. Part Ii. Step-Down Procedures For Control Of The Family-Wise Error Rate, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
U.C. Berkeley Division of Biostatistics Working Paper Series
The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rejection regions) for these test statistics and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which the …
Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi
Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi
Journal of Modern Applied Statistical Methods
The problem considered is interval estimation of the stress - strength reliability R = P(Xθ and λ respectively and a common location parameter μ . Several types of asymptotic, approximate and bootstrap intervals are investigated. Performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their usage are given.
Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We define a general statistical framework for multiple hypothesis testing and show that the correct null distribution for the test statistics is obtained by projecting the true distribution of the test statistics onto the space of mean zero distributions. For common choices of test statistics (based on an asymptotically linear parameter estimator), this distribution is asymptotically multivariate normal with mean zero and the covariance of the vector influence curve for the parameter estimator. This test statistic null distribution can be estimated by applying the non-parametric or parametric bootstrap to correctly centered test statistics. We prove that this bootstrap estimated null …