Implements the local linear kernel function.
llK_b(b,x,y, K)Matrix output with entries the values of the kernel function at each point.
A vector of design points where the kernel will be evaluated.
A vector of sample data points.
The bandwidth to use (a scalar).
The kernel function to use.
Implements the local linear kernel $$K_{x,b}(u)= \frac{K_b(u)-K_b(u)u^T D^{-1}c_1}{c_0 - c_1^T D^{-1} c_1}, $$ where \(c_1 = (c_{11}, \dots, c_{1d})^T, D = (d_{ij})_{(d+1) \times (d+1)}\) with $$ c_0 = \sum_{i=1}^n \int_0^T K_b(x-X_i(s)) Z_i(s)ds, \\ c_{ij} = \sum_{i=1}^n \int_0^T K_b(x-X_i(s))\{x-X_{ij}(s)\} Z_i(s)ds, \\ d_{jk} = \sum_{i=1}^n \int_0^T K_b(x-X_i(s))\{x-X_{ij}(s)\}\{x-X_{ik}(s)\} Z_i(s)ds, $$ see also Nielsen (1998).
tools:::Rd_expr_doi("doi:10.1080/03461238.1998.10413997")