Conditional Moments and Independence
AbstractConsider two random variables X and Y. In initial probability and statistics courses, a discussion of various concepts of dissociation between X and Y is customary. These concepts typically involve independence and uncorrelatedness. An example is shown where E(Y^n|X) = E(Y^n) and E(X^n|Y) = E(X^n) for n = 1, 2,â¦ and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence. and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence.
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Bibliographic InfoArticle provided by American Statistical Association in its journal The American Statistician.
Volume (Year): 62 (2008)
Issue (Month): (August)
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- A2 - General Economics and Teaching - - Economic Education and Teaching of Economics
- C00 - Mathematical and Quantitative Methods - - General - - - General
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- Pindyck, Robert S & Rotemberg, Julio J, 1993. "The Comovement of Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 108(4), pages 1073-1104, November.
- Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
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