On Least Squares Linear Regression Without Second Moment

  • Rajeshwari Majumdar University of Connecticut

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.

Published
2018-06-25
How to Cite
MAJUMDAR, Rajeshwari. On Least Squares Linear Regression Without Second Moment. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, june 2018. ISSN 2378-5810. Available at: <https://mjum.math.umn.edu/index.php/mjum/article/view/72>. Date accessed: 23 aug. 2019.
Section
Articles