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Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…

In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables…

Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…

In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…

If uncorrelated random variables have a common expected value and decreasing variances then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable Variance Reduction Property…

The partial least squares (PLS) is a popular modeling technique commonly used in social sciences. The traditional PLS algorithm deals with variables measured on interval scales while data are often collected on ordinal scales: a…

Multifractal theory provides a new spatial analytical tool to describe urban form and growth, but many basic problems remain to be solved. Among various pending issues, the most significant one is how to obtain proper multifractal dimension…

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…

Randomized experiments are the gold standard for causal inference, and justify simple comparisons across treatment groups. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This…

Estimation and inference in statistics pose significant challenges when data are collected adaptively. Even in linear models, the Ordinary Least Squares (OLS) estimator may fail to exhibit asymptotic normality for single coordinate…

Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an…

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 propose logit-based IV and augmented logit-based IV estimators that serve as alternatives to the traditionally used 2SLS estimator in the model where both the endogenous treatment variable and the corresponding instrument are binary. Our…

Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression-the…

For learned models to be trustworthy, it is essential to verify their robustness to perturbations in the training data. Classical approaches involve uncertainty quantification via confidence intervals and bootstrap methods. In contrast,…

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…

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of…

Ordinary differential equations provide an attractive framework for modeling temporal dynamics in a variety of scientific settings. We show how consistent estimation for parameters in ODE models can be obtained by modifying a direct…

We reassess the use of linear models to approximate response probabilities of binary outcomes, focusing on average partial effects (APE). We confirm that linear projection parameters coincide with APEs in certain scenarios. Through…

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…