R/discrete_optimal.r

In kernopt: Estimating Count Data Distributions with Discrete Optimal Symmetric Kernel

#' Discrete optimal kernel
##########################
#'
#'
#' @param x the target point at which the density is calculated
#' @param z the vector of observations
#' @param h the bandwidth (or smoothing parameter), which should match the
#'          condition (3 / 5) * (1 - 1 / k)) < h < 1
#' @param k the integer (positive) parameter that defined the support of
#'          the kernel function
#' @return Returns the value of the associated kernel function according to
#'         the target x and the bandwidth h.
#' @export
#'
#' @examples
#' discrete_optimal(x = 25, z = 1:50, h = 0.9, k = 20)
#'
discrete_optimal <- function(x, z, h, k) {
  # Return an error if h does not match the following condition:
  # (3 / 5) * (1 - 1 / k)) < h < 1
  stopifnot((h > (3 / 5) * (1 - 1 / k)), (h < 1))

  lambda <- 15 * (1 - h) / ((2 * k + 1) * (4 * k^2 + 4 * k - 3))

  target_in_support <- (abs(x - z) <= k)
  optimal_kernel <- ifelse(target_in_support,
    lambda * ((3 * k^2 + 3 * k - 1) / 5 - (x - z)^(2)) + h / (2 * k + 1),
    0
  )


  return(optimal_kernel)
}