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dMLE <- function(X, W, psi_o = NA, prec = 1e-7){
# dMLE computes vector psi s.t. the function L, defined as
#
# L(psi) := sum(W * psi) - sum_{k = 1} ^ {m - 1} J(psi_k, psi_(k + 1))
# + sum_{k = 2} ^ {m - 1} exp(psi_k)
#
# is maximized.
#
# INPUT
# - X : vector (X_1 < ... < X_m) of observations
# - W : vector of weights that sum to one
# - psi_o : initialization vector (optional)
#
# OUTPUT
# - psi : vector that maximizes L below
# - L : value of L at psi
#
#
# Version 17.10.07, Kathrin Weyermann
# Ported to R by Kaspar Rufibach, October 2010
########################################################################
# initialization
m <- length(X)
dX <- diff(X)
if (identical(psi_o, NA)){psi_o <- log(1 / m[1]) * rep(1, m)}
psi <- psi_o
L <- LikFunk(W, psi, dX)
iterDMLE <- 0
stepDirection <- Direction(W, psi, dX)
norm2 <- sum(stepDirection ^ 2)
while ((norm2 > prec) & (iterDMLE < 50)){
iterDMLE <- iterDMLE + 1
stepSize <- StepSize(W, psi, dX, stepDirection)
psi <- psi + stepSize * stepDirection
L <- LikFunk(W, psi, dX)
stepDirection <- Direction(W, psi, dX)
norm2 <- sum(stepDirection ^ 2)
} # end while
res <- list("psi" = psi, "L" = L)
return(res)
}
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