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6. Regression estimation
Given two real random variables X and Y admitting a moment of order 2, the (non-linear) regression of Y on X is the function r such that :
where G is the family of functions g such that g(X) admits a moment of order 2.
So r (X) is the best approximation of Y by a function of X. This is said to be the conditional expectation of Y knowing X and is written as :
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