1,721,333 research outputs found
Generalized Augmentation for Control of the k-Familywise Error Rate
Full text linkWhen performing many hypothesis tests at once a correction for multiplicity is needed to both keep under control the number of false discoveries and be able to detect the true departures from the null hypotheses. A recently introduced method which has been proved to be useful in genomics, neuroimaging and other fields consists in probabilistically controlling that the number of falsely rejected hypotheses does not exceed a pre-specified (low) . We introduce a new multiple testing procedure which is based on the idea of generalized augmentation: at first a number of hypotheses is rejected without any correction, then this number is adjusted by adding or removing rejections. The procedure is shown to keep under control the probability of or more false rejections. We show a small simulation study which suggests that the new procedure is very powerful, especially when the number of tests at stake is large. We conclude with an illustration on a benchmark data set on classification of colon cancer
A Review of Modern Multiple Hypothesis Testing, with particular attention to the false discovery proportion
Full text linkIn the last decade a growing amount of statistical research has been devoted to multiple testing, motivated by a variety of applications in medicine, bioinformatics, genomics, brain imaging, etc. Research in this area is focused on developing powerful procedures even when the number of tests is very large. This paper attempts to review research in modern multiple hypothesis testing with particular attention to the false discovery proportion, loosely defined as the number of false rejections divided by the number of rejections. We review the main ideas, stepwise and augmentation procedures; and resampling based testing. We also discuss the problem of dependence among the test statistics. Simulations make a comparison between the procedures and with Bayesian methods. We illustrate the procedures in applications in DNA microarray data analysis. Finally, few possibilities for further research are highlighted
Robust Constrained Clustering in Presence of Entry-Wise Outliers
No full textWe propose a robust heteroscedastic model-based clustering method based on snipping. An observation is snipped when some of its dimensions are discarded, but the remaining are used for estimation. An expectation-maximization algorithm augmented with a stochastic optimization step is used to derive inference, and its convergence properties are studied. We show global robustness of our resulting sclust procedure also when outliers arise entry-wise. The method is robust to contamination, even when most or even all of the observations contain outliers. Simulations and two real data applications illustrate and compare the approach with existing methods
Quantile regression for longitudinal data based on latent Markov subject-specific parameters
No full textWe propose a latent Markov quantile regression model for longitudinal data with non-informative drop-out. The observations, conditionally on covariates, are modeled through an asymmetric Laplace distribution. Random effects are assumed to be time-varying and to follow a first order latent Markov chain. This latter assumption is easily interpretable and allows exact inference through an ad hoc EM-type algorithm based on appropriate recursions. Finally, we illustrate the model on a benchmark data set
Unified Conditional Frequentist and Bayesian Testing: Computations in Practice and Sample Size Determination
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Snipping for robust k-means clustering under component-wise contamination
No full textWe introduce the concept of snipping, complementing that of trimming, in robust cluster analysis. An observation is snipped when some of its dimensions are discarded, but the remaining are used for clustering and estimation. Snipped k-means is performed through a probabilistic optimization algorithm which is guaranteed to converge to the global optimum. We show global robustness properties of our snipped k-means procedure. Simulations and a real data application to optical recognition of handwritten digits are used to illustrate and compare the approach. © 2013 Springer Science+Business Media New York
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