Ichimura semiparametric least squares

\(\hat\beta = \arg\min_{|b_1|=1} \sum (Y_i - \hat G_{-i,b}(X_i'b))^2\), using the existing .hrz_nw_loo leave-one-out smoother. The \(|b_1| = 1\) normalisation is required because the index scale is not identified, and leaving i out prevents the criterion collapsing by interpolation. beta is root-n even though G is not. Mirrors morie.fn.hrzich and hrznls.

Usage

morie_ichimura(X, y, h = NULL)

Arguments

X

numeric covariate matrix.

y

numeric response.

h

bandwidth.

Value

list: beta, sse, converged, root_n, n, d.

References

Horowitz, Ch. 2 (Ichimura 1993).

Examples

set.seed(1)
X <- matrix(rnorm(200), ncol = 2)
morie_ichimura(X, tanh(X %*% c(1, -0.6)))$beta[1]
#> [1] 1