相关论文: On the existence of powerful p-values and e-values…
We consider testing a composite null hypothesis $\mathcal{P}$ against a point alternative $\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\mathbb{E}_\mathsf{P}[X] \leq 1$ for every $\mathsf{P} \in…
Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…
Confidence sequences, anytime p-values (called p-processes in this paper), and e-processes all enable sequential inference for composite and nonparametric classes of distributions at arbitrary stopping times. Examining the literature, one…
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…
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…
We revisit a fundamental question in hypothesis testing: given two sets of probability measures $\mathcal{P}$ and $\mathcal{Q}$, when does a nontrivial (i.e. strictly unbiased) test for $\mathcal{P}$ against $\mathcal{Q}$ exist? Le Cam…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal…
We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $\epsilon$ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary…
The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger…
$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$…
Consider the triplet $(E, \mathcal{P}, \pi)$, where $E$ is a finite ground set, $\mathcal{P} \subseteq 2^E$ is a collection of subsets of $E$ and $\pi : \mathcal{P} \rightarrow [0,1]$ is a requirement function. Given a vector of marginals…
We study how to combine p-values and e-values, and design multiple testing procedures where both p-values and e-values are available for every hypothesis. Our results provide a new perspective on multiple testing with data-driven weights:…
Let $L$ be a convex cone of real random variables on the probability space $(\Omega,\mathcal{A},P_0)$. The existence of a probability $P$ on $\mathcal{A}$ such that $$ P \sim P_0,\quad E_P \abs{X}< \infty\, \text{ and } \, E_P(X) \leq 0\,…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
On observing a sequence of i.i.d.\ data with distribution $P$ on $\mathbb{R}^d$, we ask the question of how one can test the null hypothesis that $P$ has a log-concave density. This paper proves one interesting negative and positive result:…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
We consider the problem of computing the q->p norm of a matrix A, which is defined for p,q \ge 1, as |A|_{q->p} = max_{x !=0 } |Ax|_p / |x|_q. This is in general a non-convex optimization problem, and is a natural generalization of the…
We are concerned with multiple test problems with composite null hypotheses and the estimation of the proportion $\pi_{0}$ of true null hypotheses. The Schweder-Spj\o tvoll estimator $\hat{\pi}_0$ utilizes marginal $p$-values and only works…
A composite likelihood is a combination of low-dimensional likelihood objects useful in applications where the data have complex structure. Although composite likelihood construction is a crucial aspect influencing both computing and…