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This paper proposes a new estimator for selecting weights to average over least squares estimates obtained from a set of models. Our proposed estimator builds on the Mallows model average (MMA) estimator of Hansen (2007), but, unlike MMA,…

Econometrics · Economics 2019-12-04 Kenichiro McAlinn , Kosaku Takanashi

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 article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…

Statistics Theory · Mathematics 2011-06-22 Markus Bibinger

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

The aim of the paper is to derive the numerical least-squares estimator for mean and variance of random variable. In order to do so the following questions have to be answered: (i) what is the statistical model for the estimation procedure?…

Numerical Analysis · Mathematics 2025-10-20 Tomasz Suslo

We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…

Statistics Theory · Mathematics 2019-10-17 János Marcell Benke , Gyula Pap

We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence…

Statistics Theory · Mathematics 2023-02-07 Antoine Lejay , Sara Mazzonetto

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Statistics Theory · Mathematics 2023-03-23 Reese Pathak , Martin J. Wainwright , Lin Xiao

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

Statistics Theory · Mathematics 2012-07-06 Charles J. Geyer

This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…

Methodology · Statistics 2026-02-05 Subhodeep Dey , Gopal K. Basak , Samarjit Das

This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under consideration is possible only if either the length of the…

Statistics Theory · Mathematics 2023-10-09 P. Chigansky , M. Kleptsyna

We noisily observe solutions of an ordinary differential equation $\dot u = f(u)$ at given times, where $u$ lives in a $d$-dimensional state space. The model function $f$ is unknown and belongs to a H\"older-type smoothness class with…

Statistics Theory · Mathematics 2024-07-23 Christof Schötz , Maximilian Siebel

In this paper we study the distribution function $P(u_{\alpha})$ of the estimators $u_{\alpha} \sim T^{-1} \int^T_0 \, \omega(t) \, {\bf B}^2_{t} \, dt$, which optimise the least-squares fitting of the diffusion coefficient $D_f$ of a…

Statistical Mechanics · Physics 2015-06-12 Denis Boyer , David S. Dean , Carlos Mejia-Monasterio , Gleb Oshanin

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

Statistics Theory · Mathematics 2019-06-26 Matthew J. Holland

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…

Machine Learning · Statistics 2016-02-11 Siheng Chen , Rohan Varma , Aarti Singh , Jelena Kovačević

Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…

Methodology · Statistics 2025-03-28 Alexander Kostinski , Glenn Ierley , Sarah Kostinski

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion…

Statistics Theory · Mathematics 2013-05-07 Yuta Koike

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…

Systems and Control · Electrical Eng. & Systems 2023-09-07 Xinghua Zhu , Zhixin Liu

Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…

Statistics Theory · Mathematics 2023-12-25 Chris A. J. Klaassen