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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…
In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
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…
Understanding the how the distribution of an economic outcome, such as income, changes with respect to space and covariates is a key concern for policy makers. To address this, we develop a Bayesian nonparametric model, the Normalised…
Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
Ordinary least squares (OLS) estimators are widely used in network experiments to estimate spillover effects. We study the causal interpretation of, and inference for the OLS estimator under both design-based uncertainty from random…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
In estimating spillover effects under network interference, practitioners often use linear regression with either the number or fraction of treated neighbors as regressors. An often overlooked fact is that the latter is undefined for units…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
The presence of units with extreme values in the dependent and/or independent variables (i.e., vertical outliers, leveraged data) has the potential to severely bias regression coefficients and/or standard errors. This is common with short…
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
This paper introduces tools for assessing the sensitivity, to unobserved confounding, of a common estimator of the causal effect of a treatment on an outcome that employs weights: the weighted linear regression of the outcome on the…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…