Related papers: Combining individually valid and conditionally i.i…
Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on…
Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a…
When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most…
A/B tests are typically analyzed via frequentist p-values and confidence intervals; but these inferences are wholly unreliable if users endogenously choose samples sizes by *continuously monitoring* their tests. We define *always valid*…
U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they…
We review the methods to combine several measurements, in the form of parameter values or $p$-values.
P values or risk ratios from multiple, independent studies, observational or randomized, can be computationally combined to provide an overall assessment of a research question in meta-analysis. There is a need to examine the reliability of…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common…
The author's recent research papers, "Cumulative deviation of a subpopulation from the full population" and "A graphical method of cumulative differences between two subpopulations" (both published in volume 8 of Springer's open-access…
In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values…
The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of…
In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of…
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…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
We present the expected values from p-value hacking as a choice of the minimum p-value among $m$ independents tests, which can be considerably lower than the "true" p-value, even with a single trial, owing to the extreme skewness of the…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
The two-trials rule in drug regulation requires statistically significant results from two pivotal trials to demonstrate efficacy. However, it is unclear how the effect estimates from both trials should be combined to quantify the drug…