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We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…

Statistics Theory · Mathematics 2019-07-30 Michael Law , Ya'acov Ritov

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

Statistics Theory · Mathematics 2014-11-03 Lucien Birgé

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…

Statistics Theory · Mathematics 2023-09-29 Ashkan Ertefaie , Luke Duttweiler , Brent A. Johnson , Mark J. van der Laan

We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…

Statistics Theory · Mathematics 2020-06-29 Clément de Chaisemartin , Xavier D'Haultfœuille

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

Machine Learning · Statistics 2024-01-24 T. Tony Cai , Hongming Pu

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Statistics Theory · Mathematics 2025-04-16 Mika Meitz , Alexander Shapiro

The recent measurement of an anomalous like-sign dimuon asymmetry by the D0 collaboration has prompted theoretical speculation on possible sources of physics beyond the Standard Model that may affect lifetimes and lifetime differences in…

High Energy Physics - Phenomenology · Physics 2015-10-19 Tim Gershon

We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…

Statistics Theory · Mathematics 2018-08-22 Sara van de Geer

In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of $n$ distributions, given one single sample from each distribution. This paper studies mean estimation for entangled…

Machine Learning · Computer Science 2020-07-14 Yingyu Liang , Hui Yuan

Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…

Statistics Theory · Mathematics 2023-06-21 Elad Romanov , Gil Kur , Boaz Nadler

We study parameter inference in simulation-based stochastic models where the analytical form of the likelihood is unknown. The main difficulty is that score evaluation as a ratio of noisy Monte Carlo estimators induces bias and instability,…

Machine Learning · Statistics 2025-10-31 Zehao Li , Zhouchen Lin , Yijie Peng

This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under…

Statistics Theory · Mathematics 2026-03-03 Yuzo Maruyama

Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…

Information Theory · Computer Science 2012-04-26 Mikko Vehkaperä , Saikat Chatterjee , Mikael Skoglund

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

Statistics Theory · Mathematics 2013-11-05 Samuel Vaiter , Charles Deledalle , Gabriel Peyré , Charles Dossal , Jalal Fadili

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…

Statistics Theory · Mathematics 2025-03-04 Licong Lin , Koulik Khamaru , Martin J. Wainwright

We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…

Machine Learning · Statistics 2008-05-21 Dapo Omidiran , Martin J. Wainwright

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

Methodology · Statistics 2016-05-03 Juhee Cho , Donggyu Kim , Karl Rohe

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

Statistics Theory · Mathematics 2012-11-02 Jérémie Bigot , Theofanis Sapatinas

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

Methodology · Statistics 2019-05-28 Arun Kumar Kuchibhotla , Rohit Kumar Patra

We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and columns. We consider the least squares…

Statistics Theory · Mathematics 2015-11-03 Sabyasachi Chatterjee , Adityanand Guntuboyina , Bodhisattva Sen