On Least Squares Linear Regression Without Second Moment
Statistics Theory
2018-08-06 v1 Statistics Theory
Abstract
If X and Y are real valued random variables such that the first moments of X, Y, and XY exist and the conditional expectation of Y given X is an affine function of X, then the intercept and slope of the conditional expectation equal the intercept and slope of the least squares linear regression function, even though Y may not have a finite second moment. As a consequence, the affine in X form of the conditional expectation and zero covariance imply mean independence.
Keywords
Cite
@article{arxiv.1710.06566,
title = {On Least Squares Linear Regression Without Second Moment},
author = {Rajeshwari Majumdar},
journal= {arXiv preprint arXiv:1710.06566},
year = {2018}
}