scholarly journals Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xin Yan ◽  
Xiaogang Su
Keyword(s):  
Confidence Intervals ◽  
Error Rate ◽  
Pairwise Comparisons ◽  
Simultaneous Inference ◽  
Familywise Error Rate ◽  
Linear Combinations ◽  
Simultaneous Confidence Intervals ◽  
Nominal Level ◽  
Equal Variance ◽  
Heteroscedastic Errors

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method.

scholarly journals Pairwise comparisons for parallel profile models with mixed effects

2012 ◽  
Vol 51 (1) ◽  
pp. 67-73
Author(s):  
Hiroto Hyakutake
Keyword(s):  
Confidence Intervals ◽  
Random Effects ◽  
Nonlinear Models ◽  
Mixed Effects ◽  
Repeated Measurements ◽  
Pairwise Comparisons ◽  
Simultaneous Confidence Intervals ◽  
Regression Parameters ◽  
The Mean ◽  
Linear And Nonlinear

ABSTRACT There are several linear and nonlinear models for analyzing repeated measurements. The mean response for an individual depends on the regression parameters specific to that individual. One of the simple forms is the sum of vectors of fixed parameters and random effects. When the models with mixed effects for several groups are parallel, pairwise comparisons of level differences are considered. For the comparisons, approximate simultaneous confidence intervals are given.

scholarly journals Simultaneous confidence intervals for all pairwise comparisons of the means of delta-lognormal distributions with application to rainfall data

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0253935
Author(s):  
Patcharee Maneerat ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Rainy Season ◽  
Direct Action ◽  
Parametric Bootstrap ◽  
Rainfall Data ◽  
Pairwise Comparisons ◽  
Simultaneous Confidence Intervals ◽  
Lognormal Distributions ◽  
Natural Rainfall ◽  
Fiducial Generalized Confidence Interval

Natural disasters such as flooding and landslides are important unexpected events during the rainy season in Thailand, and how to direct action to avoid their impacts is the motivation behind this study. The differences between the means of natural rainfall datasets in different areas can be estimated using simultaneous confidence intervals (SCIs) for pairwise comparisons of the means of delta-lognormal distributions. Our proposed methods are based on a parametric bootstrap (PB), a fiducial generalized confidence interval (FGCI), the method of variance estimates recovery (MOVER), and Bayesian credible intervals based on mixed (BCI-M) and uniform (BCI-U) priors. Their coverage probabilities, lower and upper error probabilities, and relative average lengths were used to evaluate and compare their SCI performances through Monte Carlo simulation. The results show that BCI-U and PB work well in different situations, even with large differences in variances σ j 2. All of the methods were applied to estimate pairwise differences between the means of natural rainfall data from five areas in Thailand during the rainy season to determine their abilities to predict occurrences of flooding and landslides.

scholarly journals The Romano–Wolf multiple-hypothesis correction in Stata

2020 ◽  
Vol 20 (4) ◽  
pp. 812-843
Author(s):  
Damian Clarke ◽  
Joseph P. Romano ◽  
Michael Wolf
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Original Data ◽  
Dependence Structure ◽  
Familywise Error Rate ◽  
Testing Procedures ◽  
Multiple Testing Procedures ◽  
Multiple Hypothesis ◽  
Wide Range ◽  
Performance Gains

When considering multiple-hypothesis tests simultaneously, standard statistical techniques will lead to overrejection of null hypotheses unless the multiplicity of the testing framework is explicitly considered. In this article, we discuss the Romano–Wolf multiple-hypothesis correction and document its implementation in Stata. The Romano–Wolf correction (asymptotically) controls the familywise error rate, that is, the probability of rejecting at least one true null hypothesis among a family of hypotheses under test. This correction is considerably more powerful than earlier multiple-testing procedures, such as the Bonferroni and Holm corrections, given that it takes into account the dependence structure of the test statistics by resampling from the original data. We describe a command, rwolf, that implements this correction and provide several examples based on a wide range of models. We document and discuss the performance gains from using rwolf over other multiple-testing procedures that control the familywise error rate.

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