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Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
False discovery rate (FDR) is a common way to control the number of false discoveries in multiple testing. There are a number of approaches available for controlling FDR. However, for functional test statistics, which are discretized into…
Consider the problem of testing multiple null hypotheses. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($FWER$), the probability of even one…
By restricting the possible values of the proportion of null hypotheses that are true, the local false discovery rate (LFDR) can be estimated using as few as one comparison. The proportion of proteins with equivalent abundance was estimated…
Some large scale inference problems are considered based on using the relative belief ratio as a measure of statistical evidence. This approach is applied to the multiple testing problem. A particular application of this is concerned with…
The following proposition is justified from several different points of view. If you use P = 0.05 to suggest that you have made a discovery, you will be wrong at least 30 percent of the time. If, as is often the case, experiments are…
Inequalities are key tools to prove FDR control of a multiple test. The present paper studies upper and lower bounds for the FDR under various dependence structures of p-values, namely independence, reverse martingale dependence and…
The most popular multiple testing procedures are stepwise procedures based on $P$-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy. Statist.…
We study a statistical framework for replicability based on a recently proposed quantitative measure of replication success, the sceptical $p$-value. A recalibration is proposed to obtain exact overall Type-I error control if the effect is…
Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that…
This paper presents a hypothesis testing method given independent samples from a number of connected populations. The method is motivated by a forestry project for monitoring change in the strength of lumber. Traditional practice has been…
For randomized controlled trials (RCTs) with a single intervention being measured on multiple outcomes, researchers often apply a multiple testing procedure (such as Bonferroni or Benjamini-Hochberg) to adjust $p$-values. Such an adjustment…
With the pandemic, many experimental psychologists and linguists have started to collect data over the internet (hereafter on-line data). The feasibility of such experiments and the sample sizes required to achieve sufficient statistical…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
In the high dimensional regression analysis when the number of predictors is much larger than the sample size, an important question is to select the important variable which are relevant to the response variable of interest. Variable…
Given a multiple testing situation, the null hypotheses that appear to have sufficiently low probabilities of truth may be rejected using a simple, nonparametric method of decision theory. This applies not only to posterior levels of…
Negative control is a common technique in scientific investigations and broadly refers to the situation where a null effect (''negative result'') is expected. Motivated by a real proteomic dataset, we will present three promising and…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…
In recent years, multiple hypothesis testing has come to the forefront of statistical research, ostensibly in relation to applications in genomics and some other emerging fields. The false discovery rate (FDR) and its variants provide very…