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We consider asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state $\ket{\Psi}$ and the completely mixed state under one-way LOCC (local operations and…

Quantum Physics · Physics 2024-09-10 Masahito Hayashi , Masaki Owari

Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds…

Statistics Theory · Mathematics 2015-10-15 Ery Arias-Castro , Sébastien Bubeck , Gábor Lugosi , Nicolas Verzelen

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction…

Statistics Theory · Mathematics 2019-12-02 Boualem Djehiche , Othmane Mazhar , Cristian R. Rojas

This paper studies the problem of robust signal detection in Gaussian noise under quadratically convex orthosymmetric (QCO) constraints. We consider a minimax testing framework where the signal belongs to a QCO set and is separated from…

Statistics Theory · Mathematics 2026-02-17 Yikun Li , Matey Neykov

We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a…

Statistics Theory · Mathematics 2011-08-15 Olivier Catoni

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Probability · Mathematics 2020-01-03 Marina Riabiz , Tohid Ardeshiri , Ioannis Kontoyiannis , Simon Godsill

This paper considers the general signal detection and parameter estimation problem in the presence of colored Gaussian noise disturbance. By modeling the disturbance with an autoregressive process, we present three signal detectors with…

Data Analysis, Statistics and Probability · Physics 2016-07-29 Bo Tang , Haibo He , Steven Kay

In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…

Statistics Theory · Mathematics 2010-02-17 Axel Munk , Johannes Schmidt-Hieber

We study the problem of fitting parametrized curves to noisy data. Under certain assumptions (known as Cartesian and radial functional models), we derive asymptotic expressions for the bias and the covariance matrix of the parameter…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 N. Chernov , C. Lesort

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

Statistics Theory · Mathematics 2022-09-28 Wenlong Mou , Martin J. Wainwright , Peter L. Bartlett

We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…

Statistics Theory · Mathematics 2025-06-19 Thomas B. Berrett

The detection problem in statistical signal processing can be succinctly formulated: Given m (possibly) signal bearing, n-dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only…

Information Theory · Computer Science 2009-02-26 N. Raj Rao , Jack W. Silverstein

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

Statistics Theory · Mathematics 2010-11-10 Victor Konev , Serguei Pergamenchtchikov

The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce…

Statistics Theory · Mathematics 2024-01-29 Vladimir Vovk , Ruodu Wang

In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a…

Methodology · Statistics 2024-04-05 Kosuke Morikawa , Yoshikazu Terada , Jae Kwang Kim

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

Statistics Theory · Mathematics 2023-11-22 Trung Dang , Jasper C. H. Lee , Maoyuan Song , Paul Valiant

Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the…

Statistics Theory · Mathematics 2008-12-18 Leonid Galtchouk , Serguey Pergamenshchikov

We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…

Statistics Theory · Mathematics 2026-04-29 Jie Xie , Dongming Huang

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…

Machine Learning · Statistics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more precise lower bound, we study semiparametric efficiency in the…

Statistics Theory · Mathematics 2014-05-07 Mathias Trabs