Estimation of the Effective Dimension Reduction Subspace

Yi = f(xi) + εi = g(Θ >xi) + εi, i = 1, . . . , n, is addressed. In the general setup we are interested in, the covariates xi ∈ R, Θ is a d×m orthogonal matrix (ΘΘ = Im∗) and g : R ∗ → R is an unknown function. To be able to estimate Π consistently, we assume that S = Im(Θ) is the smallest subspace satisfying f(xi) = f(ΠSxi), ∀i = 1, . . . , n, where ΠS… CONTINUE READING