Single-index kernel regression — morie_index

\(\hat G(v) = \sum K_h(X_i'\beta - v)Y_i / \sum K_h(X_i'\beta - v)\). Regressing on the scalar index collapses a d-dimensional smoothing problem to one dimension, restoring the \(n^{-2/5}\) rate for any d. Mirrors morie.fn.hrznwrg.

Usage

morie_index_regression(X, y, beta, h = NULL, grid = NULL)

Arguments

X: numeric matrix of covariates.
y: numeric response.
beta: index coefficients.
h: bandwidth on the index scale.
grid: optional evaluation points on the index scale; passed to morie_nw_regression(), which chooses a default when NULL.

Value

list: index_grid, G, index, bandwidth, rate_exponent, d.

References

Horowitz, Ch. 2.

Examples

set.seed(1)
X <- matrix(rnorm(200), ncol = 2)
morie_index_regression(X, rnorm(100), c(1, -0.5))$rate_exponent
#> [1] -0.4