Mean dependence

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In probability theory, a random variable 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.[1][2]; 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[citation needed] to have a middle ground between the strong assumption of independent random variables () and the weak assumption of uncorrelated random variables

Further reading[edit]

  • Cameron, A. Colin; Trivedi, Pravin K. (2009). Microeconometrics: Methods and Applications (8th ed.). New York: Cambridge University Press. ISBN 9780521848053.
  • Wooldridge, Jeffrey M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). London: The MIT Press. ISBN 9780262232586.

References[edit]

  1. ^ Cameron & Trivedi (2009, p. 23)
  2. ^ Wooldridge (2010, pp. 54, 907)