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| | In [[probability theory]], a [[random variable]] ''Y'' is said to be '''mean independent''' of random variable ''X'' if and only if E(''Y''|''X'') = E(''Y'') for all ''x'' such that ''ƒ''<sub>1</sub>(''x'') is not equal to zero. ''Y'' is said to be '''mean dependent''' if ''E''(''Y''|''X'') ≠ ''μ''(''y'') for some ''x'' such that ''ƒ''<sub>1</sub>(''x'') is not equal to zero.{{clarify|date=April 2012}} |
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| | According to {{Harvtxt|Cameron and Trivedi|2009|p=23}} and {{Harvtxt|Wooldridge|2010|pp=54, 907}}, [[independence (probability theory)|Stochastic independence]] implies mean independence, but the converse is not necessarily true. |
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| | Moreover, mean independence implies uncorrelation while the converse is not necessarily true. |
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| | The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent distributions <math>f_{X_1}\perp{}f_{X_2}</math> and the weak assumption of uncorrelated variables <math>\text{Cov}(X_1,X_2)=0</math> of a pair of random variables <math>X_1</math> and <math>X_2</math>. |
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| | If ''X'', ''Y'' are two different random variables such that ''X'' is mean independent of ''Y'' and ''Z=f(X)'', which means that ''Z'' is a function only of ''X'', then ''Y'' and ''Z'' are mean independent. |
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| | ==References== |
| | *{{cite book |last=Cameron |first=A. Colin |first2=Pravin K. |last2=Trivedi |year=2009 |title=Microeconometrics: Methods and Applications |location=New York |publisher=Cambridge University Press |edition=8th |isbn=9780521848053 |ref=harv }} |
| | *{{cite book |last=Wooldridge |first=Jeffrey M. |year=2010 |title=Econometric Analysis of Cross Section and Panel Data |location=London |publisher=The MIT Press |edition=2nd |isbn=9780262232586 |ref=harv }} |
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| | {{DEFAULTSORT:Mean dependence}} |
| | [[Category:Probability theory]] |
| | [[Category:Statistical terminology]] |
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| | {{Probability-stub}} |
Revision as of 21:49, 3 February 2014
Template:Multiple issues
In probability theory, a random variable Y is said to be mean independent of random variable X if and only if E(Y|X) = E(Y) for all x such that ƒ1(x) is not equal to zero. Y is said to be mean dependent if E(Y|X) ≠ μ(y) for some x such that ƒ1(x) is not equal to zero.Template:Clarify
According to Template:Harvtxt and Template:Harvtxt, Stochastic independence implies mean independence, but the converse is not necessarily true.
Moreover, mean independence implies uncorrelation while the converse is not necessarily true.
The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent distributions and the weak assumption of uncorrelated variables of a pair of random variables and .
If X, Y are two different random variables such that X is mean independent of Y and Z=f(X), which means that Z is a function only of X, then Y and Z are mean independent.
References
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
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- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
Template:Probability-stub