Examples of bandwidth choice in kernel density estimation

bandwidth-choice-in-kde-example.R

ptmp <- par(mfrow=c(2,2), mar = c(3,3,3,3))


set.seed(123)
n <- 7
x <- rnorm(n, sd = 3)

K <- function(x) dnorm(x)

kde <- function(x, data, h, K) {
  n <- length(data)
  out <- outer(x, data, function(xi,yi) K((xi-yi)/h))
  rowSums(out)/(n*h)
} 

xx = seq(-8, 8, by = 0.001)
for (h in c(0.25, 0.5, 0.75, 1)) {
  plot(NA, xlim = c(-4, 8), ylim = c(0, 0.5), xlab = "", ylab = "",
       main = paste0("h = ", h))
  for (i in 1:n) {
    lines(xx, K((xx-x[i])/h)/n, type = "l", col = rainbow(n)[i])
    rug(x[i], lwd = 2, col = rainbow(n)[i], side = 3, ticksize = 0.075)
  }
  lines(xx, kde(xx, x, h, K), col = "darkgray")
}

par(ptmp)