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Related papers: Stein Shrinkage and Second-Order Efficiency for se…

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The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James-Stein thresholding…

Methodology · Statistics 2011-10-06 Sylvain Sardy

Stein's formula states that a random variable of the form $z^\top f(z) - \text{div} f(z)$ is mean-zero for functions $f$ with integrable gradient. Here, $\text{div} f$ is the divergence of the function $f$ and $z$ is a standard normal…

Statistics Theory · Mathematics 2020-02-10 Pierre C Bellec , Cun-Hui Zhang

We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference…

Methodology · Statistics 2014-12-19 Aiyou Chen , Art B. Owen , Minghui Shi

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various…

Statistics Theory · Mathematics 2015-03-18 A. K. Md. Ehsanes Saleh , Enayetur Raheem

In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stochastic} extension of…

Optimization and Control · Mathematics 2020-02-25 Filip Hanzely , Nikita Doikov , Peter Richtárik , Yurii Nesterov

We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…

Statistics Theory · Mathematics 2019-11-19 Vladimir Koltchinskii , Mayya Zhilova

This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…

Statistics Theory · Mathematics 2024-02-09 Shiyuan He , Jianhua Z. Huang , Kejun He

In the setting of multi-armed trials, adaptive designs are a popular way to increase estimation efficiency, identify optimal treatments, or maximize rewards to individuals. Recent work has considered the case of estimating the effects of K…

Methodology · Statistics 2026-02-10 Evan T. R. Rosenman , Kristen B. Hunter

Let $\mathbf{x}_j = \mathbf{\theta} + \mathbf{\epsilon}_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbf{\theta},\mathbf{\Sigma})$ with unknown mean $\mathbf{\theta} \in \mathbb{R}^d$ and…

Statistics Theory · Mathematics 2020-12-23 Fan Zhou , Ping Li

Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function.…

Statistics Theory · Mathematics 2011-01-19 Reman Abu-Shanab , John T. Kent , William E. Strawderman

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

Statistics Theory · Mathematics 2007-06-13 Guang Cheng , Michael R. Kosorok

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage…

Statistics Theory · Mathematics 2009-02-23 Nicolas Privault , Anthony Réveillac

When the available information is noisy zeroth-order (ZO) oracle, stochastic approximation methods are popular for estimating the root of the multivariate gradient equation. Inspired by the Stein's identity, this work establishes a novel…

Optimization and Control · Mathematics 2021-04-06 Jingyi Zhu

The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…

Numerical Analysis · Mathematics 2023-07-04 Jun Ohkubo

A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as…

Methodology · Statistics 2025-05-14 Herbert P. Susmann , Yiting Li , Mara A. McAdams-DeMarco , Wenbo Wu , Iván Díaz

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

Methodology · Statistics 2024-02-07 Ryo Okano , Yasuyuki Hamura , Kaoru Irie , Shonosuke Sugasawa

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

Optimization and Control · Mathematics 2024-03-27 Shuyao Li , Stephen J. Wright

We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making…

Optimization and Control · Mathematics 2024-04-24 Sachin Garg , Albert S. Berahas , Michał Dereziński

Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…

Numerical Analysis · Mathematics 2020-08-04 Ruisheng Qi , Xiaojie Wang

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani