In Wikipedia , it is written that :
the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. The statistical errors on the other hand are independent, and their sum within the random sample is almost surely not zero.
But one of our assumptions are $\mathbb E(\epsilon_i)=0$ . Doesn't it imply $\sum\epsilon_i=0$ . If so , then errors
CANNOT also be independent because
Wikipedia says that $\sum e_i=0$ implies residuals are not independent .
N.B : $\epsilon$ denotes statistical error while $e$ denotes residual .
- Following this question , another question arises :
In this pdf , in the section of
MULTILEVEL ANALYSIS at very beginning it is written that :
The usual assumption is either the sample units themselves or the corresponding
RESIDUALSin some statistical model are independently and identically distributed .
Wikipedia , they have mentioned
RESIDUALS are not independent (i.e., dependent) .
Then how is the assumption "either the sample units themselves or the corresponding
RESIDUALS in some statistical model
are independently and identically distributed ? "