A simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic in the presence of nuisance parameters, based only on a sample generator from the distribution of interest is presented.
Abstract
We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the sense of minimum average KL-divergence of its $p$-values versus uniform and we argue that it can be expected to have good power when the dimension of the statistic equals the dimension of the parameter. It is able to incorporate prior knowledge about group invariances such as translation and scale. It can discover the one-sample $t$-test almost exactly, outperforms the Welch test in terms of worst-case size over a constrained variance-ratio range and achieves good calibration on partial biserial correlations, while showing higher power (and being much faster) on small-to-moderate samples than profile likelihood-ratio techniques.
The classical two-sample problem is framed as the detection of differences in marginal distributions, in terms of location, scale, or overall shape. In this paper, Gap–Entropy Testing (GET) is proposed, a novel nonparametric framework that extends the two-sample paradigm by adding a spacing-sensitive component to conve...
V. Karalis· Applied Mathematics and Stat...· 0 citations
These are the first procedures using moderated t-statistics that control the false discovery rate (FDR) in finite samples under independence across units and null group invariance, without assuming limma's hierarchical model.
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We present an approach for determining sample sizes required to detect underestimations of the expected shortfall with a prescribed power when applying the recently proposed e-backtesting procedure. We consider scenarios in which the value-at-risk at level $p$ is always estimated correctly, while the difference between...
It is shown that disclosure risk decreases with the size of the original dataset, but increases with the dimensionality of the feature space and the amount of synthetic information released, whether through the release of larger synthetic datasets or multiple generator realizations.
Rasmus Rask Kragh Jørgensen, A. Nøhr, Jan Reiter Sørensen et al.· 0 citations
A one-step estimator with K-fold cross-fitting and a U-statistic correction of the squared loss that removes the Monte Carlo bias of the naive plug-in is proposed, which is $\sqrt{n}$-consistent and asymptotically normal under double-robust rate conditions, and the resulting Wald interval attains nominal coverage.
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
