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A multivariable measurement error model $AX \approx B$ is considered. Here $A$ and $B$ are input and output matrices of measurements and $X$ is a rectangular matrix of fixed size to be estimated. The errors in $[A,B]$ are row-wise…

Statistics Theory · Mathematics 2017-03-17 Yaroslav Tsaregorodtsev

We consider an on-line least squares regression problem with optimal solution $\theta^*$ and Hessian matrix H, and study a time-average stochastic gradient descent estimator of $\theta^*$. For $k\ge2$, we provide an unbiased estimator of…

Machine Learning · Statistics 2025-11-18 Nabil Kahalé

We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…

Statistics Theory · Mathematics 2015-07-31 Sabyasachi Chatterjee , Adityanand Guntuboyina , Bodhisattva Sen

Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai…

Statistics Theory · Mathematics 2023-06-22 Alessandro Casini , Pierre Perron

This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…

Statistics Theory · Mathematics 2026-04-24 Vladimir Pastukhov

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…

Statistics Theory · Mathematics 2012-01-04 Benedikt M. Pötscher , Ulrike Schneider

A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…

Statistics Theory · Mathematics 2022-05-17 Christof Schötz

In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…

Methodology · Statistics 2021-06-21 Han Du , Peter M. Bentler

We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…

Instrumentation and Methods for Astrophysics · Physics 2015-11-18 Rodrigo A. Lobos , Jorge F. Silva , Rene A. Mendez , Marcos Orchard

Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…

Statistics Theory · Mathematics 2019-10-16 Arun K. Kuchibhotla , Lawrence D. Brown , Andreas Buja , Junhui Cai

In a regression setting with a response vector and given regressor vectors, a typical question is to what extent the response is related to these regressors, specifically, how well it can be approximated by a linear combination of the…

Statistics Theory · Mathematics 2025-02-03 Lutz Duembgen , Laurie Davies

In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…

Methodology · Statistics 2020-03-03 Li Cai , Lijie Gu , Qihua Wang , Suojin Wang

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…

Statistics Theory · Mathematics 2016-02-09 Marta García Bárzana , Ana Colubi , Erricos John Kontoghiorghes

Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…

This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations…

Statistics Theory · Mathematics 2024-04-22 Yacouba Boubacar Maïnassara , Eugen Ursu

We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $\alpha$-stable (S$\alpha$S) vector, we…

Information Theory · Computer Science 2026-01-15 Rayan Chouity , Charbel Hannoun , Jihad Fahs , Ibrahim Abou-Faycal

This article is a survey of the results on asymptotic behavior of small ball probabilities in $L_2$-norm. Recent progress in this field is mainly based on the methods of spectral theory of differential and integral operators.

Probability · Mathematics 2023-06-26 Alexander Nazarov , Yulia Petrova

Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…

Statistics Theory · Mathematics 2008-02-08 Joseph Ngatchou-Wandji

The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…

Statistics Theory · Mathematics 2016-08-09 Pierre C. Bellec

The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…

Probability · Mathematics 2013-01-09 Daniel Hug , Günter Last , Zbyněk Pawlas , Wolfgang Weil