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改进错误覆盖陈述率调整的置信区间AI 解读

Abstract This study addresses the challenges of inference following selection in fields like clinical trials, genome-wide association studies, and functional magnetic resonance imaging, where traditional methods like simultaneous confidence intervals (CIs) might be too conservative. We introduce an improved false coverage-statement rate controlling CIs, when the selection is done by passing a threshold in a certain direction. The CIs for the selected parameters are similar…

多个假设族的选择性推断AI 解读

Summary In many complex multiple-testing problems the hypotheses are divided into families. Given the data, families with evidence for true discoveries are selected, and hypotheses within them are tested. Neither controlling the error rate in each family separately nor controlling the error rate over all hypotheses together can assure some level of confidence about the filtration of errors within the selected families. We formulate this concern about selective inference in…

更有利于判定符号的选择调整置信区间AI 解读

In many current large-scale problems, confidence intervals (CIs) are constructed only for the parameters that are large, as indicated by their estimators, ignoring the smaller parameters. Such selective inference poses a problem to the usual marginal CIs that no longer offer the right level of coverage, not even on the average over the selected parameters. We address this problem by developing three methods to construct short and valid CIs for the location parameter of a…

独立性条件下具有 FDR 控制保证的自适应逐步下降程序AI 解读

In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m+1−i(1−q)], i=1, …, m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses.…

空间信号的错误发现率控制AI 解读

The problem of multiple testing for the presence of signal in spatial data can involve numerous locations. Traditionally, each location is tested separately for signal presence, but then the findings are reported in terms of clusters of nearby locations. This is an indication that the units of interest for testing are clusters rather than individual locations. The investigator may know a priori these more natural units or an approximation to them. We suggest testing these…

控制错误发现率的自适应线性逐步上升程序AI 解读

The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in…

通过控制错误发现率适应未知稀疏性AI 解读

We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the ℓp norm for p small. We obtain a procedure which is asymptotically minimax for ℓr loss, simultaneously throughout a range of such…

所选参数的错误发现率调整多重置信区间AI 解读

Often in applied research, confidence intervals (CIs) are constructed or reported only for parameters selected after viewing the data. We show that such selected intervals fail to provide the assumed coverage probability. By generalizing the false discovery rate (FDR) approach from multiple testing to selected multiple CIs, we suggest the false coverage-statement rate (FCR) as a measure of interval coverage following selection. A general procedure is then introduced,…

John W. Tukey 对多重比较的贡献AI 解读

This article provides a historical overview of the philosophical, theoretical and practical contributions made by John Tukey to the field of simultaneous inference. His early work, culminating in the monograph "The Problem of Multiple Comparisons," established him as one of the pioneers in the field, investing it with both academic respectability and a focus on practical problems. For many years afterward, Tukey only published sporadically in the area but remained convinced…

更不易包含零的非等变同时置信区间AI 解读

We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μ j ) n j=1 of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on…

更不易包含零的非等变同时置信区间AI 解读

We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μ j ) n j=1 of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on…

总体分布长尾时，t 检验真的保守吗？AI 解读

It is generally believed that the t test is conservative for a sample from a long-tailed symmetric distribution. Yet the probability inequalities expressing this property have not been proved. The inequalities are explored here using various criteria for long-tailedness and leaning on the geometrical interpretation of the t test. It is proved that the t test is conservative but only for large enough critical values. Examples of a liberal t test for lower values are given.…