Related papers: Capturing the Severity of Type II Errors in High-D…
While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this…
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one…
The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing…
This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…
Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…
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…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
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…
The use of weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. This paper studies weighted multiple testing in a decision-theoretic framework. We develop oracle and data-driven procedures…
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…
There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…
In clinical studies upon which decisions are based there are two types of errors that can be made: a type I error arises when the decision is taken to declare a positive outcome when the truth is in fact negative, and a type II error arises…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…
In this paper we consider the problem of multiple testing when the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather…
This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to…
When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by some selection (screening or filtering) process, and then to…