Related papers: Least Square Error Method Robustness of Computatio…
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…
We analyze the performance of a linear-equality-constrained least-squares (CLS) algorithm and its relaxed version, called rCLS, that is obtained via the method of weighting. The rCLS algorithm solves an unconstrained least-squares problem…
Linear least squares regression is subject to bias due to an omitted variable, a mismeasured regressor, or simultaneity. A simple test to detect the bias is proposed and explored in simulation and in real data sets.
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
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…
Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial…
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to reduce the size of the problem, hence reducing the…
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…
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…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
We study an $\ell_{1}$-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. Specifically, we consider the case where errors are assumed to follow an autoregressive process,…
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…