I think I understand this but I wanted to check: performing a regression by minimizing sum of squared errors produces a curve that goes through the mean of the dependent variable at each value of the independent variable (e.g. if my regression produces y=f(x) then f(x)=E[Y|X=x]). Performing a regression by minimizing the sum of absolute errors results in a curve that goes through the median value of the dependent variable.
If this is correct then an absolute error and a mean error regression should produce exactly the same results if the errors are normally distributed (as the mean and the median are the same) given a suitably large sample. However, while both absolute and sum of squared regessions produce an unbiased estimate of the mean (assuming normally distributed errors) the squared error approach produces a more efficient estimate (in other words both will converge to the mean as sample size is increased but the squared error estimate will converge more quickly). Do I have any of this right? Thanks, Oliver PS: I already posted this to alt.sci.math.statistics.prediction but then noticed that these groups are much more active. Please forgive the cross-posting. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
