Mean dependence explained
is said to be
mean independent of random variable
if and only if its
conditional mean
equals its (unconditional)
mean
for all
such that the probability density/mass of
at
,
, is not zero. Otherwise,
is said to be
mean dependent on
.
Stochastic independence implies mean independence, but the converse is not true.; moreover, mean independence implies uncorrelatedness while the converse is not true. Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for
to be mean-independent of
even though
is mean-dependent on
.
The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent random variables (
) and the weak assumption of uncorrelated random variables
(\operatorname{Cov}(X1,X2)=0).
Further reading
- Book: Cameron . A. Colin . Pravin K. . Trivedi . 2009 . Microeconometrics: Methods and Applications . New York . Cambridge University Press . 8th . 9780521848053 .
- Book: Wooldridge, Jeffrey M. . 2010 . Econometric Analysis of Cross Section and Panel Data . London . The MIT Press . 2nd . 9780262232586 .