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We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…

Econometrics · Economics 2023-04-26 Yassine Sbai Sassi

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of autoregressive moving-average (ARMA) models with regime changes under the assumption that the errors are uncorrelated but not necessarily independent.…

Statistics Theory · Mathematics 2019-07-11 Yacouba Boubacar Maïnassara , Landy Rabehasaina

In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained…

Statistics Theory · Mathematics 2009-09-11 Eric Cator

In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…

Numerical Analysis · Mathematics 2026-02-11 Kensuke Aishima

We study the monotone single index model where a real response variable $Y $ is linked to a $d$-dimensional covariate $X$ through the relationship $E[Y | X] = \Psi_0(\alpha^T_0 X)$ almost surely. Both the ridge function, $\Psi_0$, and the…

Statistics Theory · Mathematics 2018-04-19 F. Balabdaoui , C. Durot , H. Jankowski

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

Statistics Theory · Mathematics 2013-01-16 Elodie Brunel , André Mas , Angelina Roche

In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator…

Statistics Theory · Mathematics 2019-06-18 Emmanuel Caron

The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…

Statistics Theory · Mathematics 2026-02-12 Piet Groeneboom

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

Machine Learning · Statistics 2022-06-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Statistics Theory · Mathematics 2018-10-16 Michael Krikheli , Amir Leshem

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…

Probability · Mathematics 2009-06-29 Bernard Bercu , Benoite de Saporta , Anne Gegout-Petit

In this article, we present the least squares estimator for the drift parameter in a linear regression model driven by the increment of a fractional Brownian motion sampled at random times. For two different random times, Jittered and…

Statistics Theory · Mathematics 2019-02-25 Héctor Araya , Natalia Bahamonde , Lisandro Fermín , Tania Roa , Soledad Torres

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

Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…

Statistics Theory · Mathematics 2023-11-09 Mufang Ying , Koulik Khamaru , Cun-Hui Zhang

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…

Statistics Theory · Mathematics 2008-03-18 Sándor Baran , Gyula Pap

In this paper, we give a tutorial on asymptotic properties of the Least Square (LS) and Regularized Least Squares (RLS) estimators for the finite impulse response model with filtered white noise inputs. We provide three perspectives: the…

Statistics Theory · Mathematics 2022-01-03 Yue Ju , Tianshi Chen , Biqiang Mu , Lennart Ljung

Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates…

Statistics Theory · Mathematics 2024-01-01 Johannes Schmidt-Hieber , Petr Zamolodtchikov

The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations…

Statistics Theory · Mathematics 2024-03-29 David Bolin , Jonas Wallin

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true…

Econometrics · Economics 2026-05-04 Hyungsik Roger Moon , Martin Weidner

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

Statistics Theory · Mathematics 2020-05-26 Rodrigo A. González , Cristian R. Rojas