Related papers: Model-free Study of Ordinary Least Squares Linear …
In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…
Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…
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…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance…
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…
In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under…
Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.
This article deals with asimple issue: if we have grouped data with a binary dependent variable and want to include fixed effects (group specific intercepts) in the specification, is Ordinary Least Squares (OLS) in any way superior to a…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Linear regression is perhaps one of the most popular statistical concepts, which permeates almost every scientific field of study. Due to the technical simplicity and wide applicability of linear regression, attention is almost always…
Deep learning research has uncovered the phenomenon of benign overfitting for overparameterized statistical models, which has drawn significant theoretical interest in recent years. Given its simplicity and practicality, the ordinary least…