English
Related papers

Related papers: Universality laws for Gaussian mixtures in general…

200 papers

While classical in many theoretical settings - and in particular in statistical physics-inspired works - the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine…

Machine Learning · Statistics 2024-07-22 Federica Gerace , Florent Krzakala , Bruno Loureiro , Ludovic Stephan , Lenka Zdeborová

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Statistics Theory · Mathematics 2007-06-13 Yacine Ait-Sahalia , Per A. Mykland

We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish,…

Data Structures and Algorithms · Computer Science 2017-09-08 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…

Statistics Theory · Mathematics 2025-05-09 Ruijian Han , Yiming Xu

A recent line of work provides new statistical tools based on game-theory and achieves safe anytime-valid inference without assuming regularity conditions. In particular, the framework of universal inference proposed by Wasserman, Ramdas…

Statistics Theory · Mathematics 2025-04-01 Hongjian Shi , Mathias Drton

The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…

Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…

Statistics Theory · Mathematics 2021-05-04 Jeffrey W. Miller

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max…

Machine Learning · Statistics 2026-04-06 Chiheb Yaakoubi , Cosme Louart , Malik Tiomoko , Zhenyu Liao

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…

Methodology · Statistics 2021-05-18 Tatsuya Kubokawa , Shonosuke Sugasawa , Hiromasa Tamae , Sanjay Chaudhuri

We study the joint distribution of SYK Hamiltonians for different systems with specified overlaps. We show that, in the large-system limit, their joint distribution converges in distribution to a mixed $q$-Gaussian system. We explain that…

Operator Algebras · Mathematics 2026-04-07 Weihua Liu , Haoqi Shen

We study training algorithms with data following a Gaussian mixture model. For a specific family of such algorithms, we present a non-asymptotic result, connecting the evolution of the model to a surrogate dynamical system, which can be…

Machine Learning · Computer Science 2026-03-11 Ashkan Panahi

The generalized linear model is widely used in all areas of applied statistics and while correct asymptotic inference can be achieved under misspecification of the distributional assumptions, a correctly specified mean structure is crucial…

Methodology · Statistics 2015-07-07 Klaus K. Holst

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…

Mathematical Physics · Physics 2014-03-11 Kyong-Hui Kim , Hak-Myong Pak

We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…

Methodology · Statistics 2017-10-09 Ryan P. Browne , Paul D. McNicholas

Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…

Methodology · Statistics 2017-11-15 Yuhong Wei , Yang Tang , Emilie Shireman , Paul D. McNicholas , Douglas L. Steinley

For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$. We…

Dynamical Systems · Mathematics 2024-08-05 Manfred Denker , Marc Keßeböhmer , Artur O. Lopes , Silvia R. C. Lopes

It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…

Probability · Mathematics 2024-05-28 Terence Tao , Van Vu

Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…

Information Theory · Computer Science 2020-01-22 Farhad Shirani , Siddharth Garg , Elza Erkip

The Generalized Mallows Model (GMM) is a well known family of models for ranking data. A GMM is a distribution over $\mathbb{S}_n$, the set of permutations of n objects, characterized by a location parameter $\sigma \in \mathbb{S}_n$, known…

Statistics Theory · Mathematics 2025-03-25 Marina Meilă