Analysis of Least square estimator for simple Linear Regression with a uniform distribution error
M Jlibene (Modeling, Simulation, and Data Analysis), S Taoufik, (Modeling, Simulation, and Data Analysis), S Benjelloun (Modeling,, Simulation, and Data Analysis, CMLA)
TL;DR
This paper investigates the properties of the least squares estimator in simple linear regression when the error term follows a uniform distribution, providing its distribution law and convergence analysis.
Contribution
It introduces the distribution law of the least squares estimator under uniform errors and establishes its convergence properties, which are novel in this context.
Findings
Derived the law of the least squares estimator with uniform errors
Proved convergence properties of the estimator under this setting
Enhanced understanding of estimator behavior with non-normal errors
Abstract
We study the least square estimator, in the framework of simple linear regression, when the deviance term with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator, and prove some convergence properties.
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Taxonomy
TopicsStatistical Methods and Inference · Bayesian Methods and Mixture Models · Random Matrices and Applications