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Article | REF: AF603 V1

Functional estimation

Author: Denis BOSQ

Publication date: October 10, 2009

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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 :

E(Y−r(X))2≤E(Y−g(X))2, g∈G

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...

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