R/LocalVariance.r

In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

LocalVariance <- function(x, w = NULL, phi) {
  n <- length(x)
  if (is.null(w)) {
    p <- rep(1 / n, n)
  } else {
    p <- w / sum(w)
  }

  m <- sum(p * x)

  dx <- diff(x)
  s2a <- sum(dx * (x[1:(n - 1)] - m)^2 * J10(phi[1:(n - 1)], phi[2:n]))
  s2b <- sum(dx * (x[2:n] - m)^2 * J10(phi[2:n], phi[1:(n - 1)]))
  s2c <- sum(dx^3 * J11(phi[1:(n - 1)], phi[2:n]))

  s2 <- s2a + s2b - s2c

  return(s2)
}