Functional estimation : Regression estimation

Regression estimation
Functional estimation

Author : Denis BOSQ

Publication date: October 10, 2009 | Lire en français

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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} \leq E {(Y - g (X))}^{2}, g \in 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 Y by a function of X. This is said to be the conditional...

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Ongoing reading
Regression estimation

(1) - BERLINET (A.), DEVROYE (L) - A comparison of kernel density estimates - Publ. Inst. Statist. Univ. Paris, 38 (3), p. 3-59 (1994).
(2) - BLANKE (D.), PUMO (B.) - Optimal sampling for density estimation in continuous time - J. Time Ser. Anal., 24 (1), p. 1-24...

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