Related papers: Universal Inference Meets Random Projections: A Sc…
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference…
Le Cam's third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic $T_n$ under a non-null sequence of probability measures $\{Q_n\}$, provided its limiting distribution under a null…
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem,…
Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly…
Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars:…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…
We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine.…
We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and $s$-concave densities on $\mathbb{R}$. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse…
We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…
We propose a likelihood ratio statistic for forming hypothesis tests and confidence intervals for a nonparametrically estimated univariate regression function, based on the shape restriction of concavity (alternatively, convexity). Dealing…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…
The problem of characterizing a multivariate distribution of a random vector using examination of univariate combinations of vector components is an essential issue of multivariate analysis. The likelihood principle plays a prominent role…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…