Vectorised kernel functions on the support |u| <= 1 (Gaussian is on
the real line). Used by RDD local-linear estimators and friends for
kernel weighting around the cutoff.
Usage
morie_rdd_kernel_triangular(u)
morie_rdd_kernel_epanechnikov(u)
morie_rdd_kernel_uniform(u)
morie_rdd_kernel_gaussian(u)
Arguments
- u
Numeric vector of standardised distances from the cutoff
(i.e. \((x - c)/h\)).
Value
Numeric vector of kernel weights, same length as u.
A function of one argument returning Epanechnikov kernel weights.
A function of one argument returning uniform kernel weights.
A function of one argument returning Gaussian kernel weights.
Details
morie_rdd_kernel_triangular: \(K(u) = \max(1 - |u|, 0)\)
morie_rdd_kernel_epanechnikov: \(K(u) = (3/4)(1 - u^2)\) on |u| <= 1
morie_rdd_kernel_uniform: \(K(u) = 1/2\) on |u| <= 1
morie_rdd_kernel_gaussian: \(K(u) = \phi(u)\), the standard normal density
Examples
morie_rdd_kernel_epanechnikov(seq(-1, 1, by = 0.5))
#> [1] 0.0000 0.5625 0.7500 0.5625 0.0000
morie_rdd_kernel_uniform(seq(-2, 2, by = 1))
#> [1] 0.0 0.5 0.5 0.5 0.0
morie_rdd_kernel_gaussian(seq(-1, 1, by = 0.5))
#> [1] 0.2419707 0.3520653 0.3989423 0.3520653 0.2419707
