Related papers: Rao-Blackwellized e-variables
E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well…
We introduce a new sufficient statistic for the population parameter vector by allowing for the sampling design to first be selected at random amongst a set of candidate sampling designs. In contrast to the traditional approach in survey…
We derive the unique e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, hereby contributing with the first application beyond the assumption of mutually absolutely continuous…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise…
Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented.…
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective statistical test that rejects the null hypothesis as soon as…
Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to…
The e-value is gaining traction as a robust alternative to p-values and Bayes factors for quantifying statistical evidence. e-values are a promising method for adaptive clinical trials due to their anytime-validity: e-values ensure type I…
We provide a general condition under which e-variables in the form of a simple-vs.-simple likelihood ratio exist when the null hypothesis is a composite, multivariate exponential family. Such `simple' e-variables are easy to compute and…
We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant…
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our…
We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the…
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…
We develop and compare e-variables for testing whether $k$ samples of data are drawn from the same distribution, the alternative being that they come from different elements of an exponential family. We consider the GRO (growth-rate…
Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods…
Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple…
We wish to compute the gradient of an expectation over a finite or countably infinite sample space having $K \leq \infty$ categories. When $K$ is indeed infinite, or finite but very large, the relevant summation is intractable. Accordingly,…
Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…