TY - JOUR
AU - Majumdar, Rajeshwari
PY - 2018/06/25
TI - On Least Squares Linear Regression Without Second Moment
JF - Minnesota Journal of Undergraduate Mathematics; Vol 4 No 1
KW -
N2 - 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.
UR - https://mjum.math.umn.edu/index.php/mjum/article/view/72