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We propose a framework for testing the homogeneity of conditional average treatment effects (CATEs) across multiple experimental and observational studies. Our approach leverages multiple randomized trials to assess whether treatment…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
Many estimators of the variance of the well-known unbiased and uniform most powerful estimator $\htheta$ of the Mann-Whitney effect, $\theta = P(X < Y) + \nfrac12 P(X=Y)$, are considered in the literature. Some of these estimators are only…
This paper introduces the correlation-of-divergency coefficient, c-delta, a custom statistical measure designed to quantify the similarity of internal divergence patterns between two groups of values. Unlike conventional correlation…
Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…
Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to…
When conducting a meta-analysis of standardized mean differences (SMDs), it is common to assume equal variances in the two arms of each study. This leads to Cohen's $d$ estimates for which interpretation is simple. However, this simplicity…
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite…
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for…
Motivation: P values derived from the null hypothesis significance testing framework are strongly affected by sample size, and are known to be irreproducible in underpowered studies, yet no suitable replacement has been proposed. Results:…
Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…
Which type of statistical uncertainty -- statistical (in)significance with a p-value, or a Bayesian probability -- enables people to see the continuous nature of uncertainty more clearly in a policymaking context? An original survey…
Comparative binary outcome data are of fundamental interest in statistics and are often pooled in meta-analyses. Here we examine the simplest case where for each study there are two patient groups and a binary event of interest, giving rise…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
The score test statistic using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
We consider a three-level meta-analysis of standardized mean differences. The standard method of estimation uses inverse-variance weights and REML/PL estimation of variance components for the random effects. We introduce new moment-based…