Kernels: Classical (unmodified) kernel and related functionals

In HQM: Superefficient Estimation of Future Conditional Hazards Based on Marker Information

Classical (unmodified) kernel and related functionals

Description

Implements the classical kernel function and related functionals

Usage

K_b(b,x,y, K)
xK_b(b,x,y, K)
K_b_mat(b,x,y, K)

Arguments

x	A vector of design points where the kernel will be evaluated.
y	A vector of sample data points.
b	The bandwidth to use (a scalar).
K	The kernel function to use.

Details

The function K_b implements the classical kernel function calculation

h^{-1} K \left ( \frac{x-y}{h} \right )

for scalars x and y while xK_b implements the functional

h^{-1} K \left ( \frac{x-y}{h} \right )(x-y)

again for for scalars x and y. The function K_b_mat is the vectorized version of K_b. It uses as inputs the vectors (X_1, \dots, X_n) and (Y_1, \dots, Y_n) and returns a n \times n matrix with entries

h^{-1} K \left ( \frac{X_i-Y_j}{h} \right )

Value

Scalar values for K_b and xK_b and matrix outputs for K_b_mat.

HQM documentation built on Jan. 8, 2026, 9:08 a.m.