Unconstrained piecewise linear MLE
Given a vector of observations x = (x_1, …, x_m) with pairwise distinct entries and a vector of weights w =(w_1, …, w_m) s.t. ∑_{i=1}^m w_i = 1, this function computes a function \hat φ_{MLE} (represented by the vector (\hat φ_{MLE}(x_i))_{i=1}^m) supported by [x_1, x_m] such that
L(φ) = ∑_{i=1}^m w_i φ(x_i) - ∑_{j=1}^{m-1} (x_{j+1} - x_j) J(φ_j, φ_{j+1})
is maximal over all continuous, piecewise linear functions with knots in {x_1, …, x_m}.
MLE(x, w = NA, phi_o = NA, prec = 1e-7, print = FALSE)
x |
Vector of independent and identically distributed numbers, with strictly increasing entries. |
w |
Optional vector of nonnegative weights corresponding to x_m. |
phi_o |
Optional starting vector. |
prec |
Threshold for the directional derivative during the Newton-Raphson procedure. |
print |
print = TRUE outputs log-likelihood in every loop, print = FALSE does not. Make sure to tell R to output (press CTRL+W). |
phi |
Resulting column vector (\hat φ_{MLE}(x_i))_{i=1}^m. |
L |
Value L(\hat φ_{MLE}) of the log-likelihood at \hat φ_{MLE}. |
Fhat |
Vector of the same length as x with entries \hat F_{MLE,1} = 0 and \hat F_{MLE,k} = ∑_{j=1}^{k-1} (x_{j+1} - x_j) J(φ_j, φ_{j+1}) for k >= 2. |
This function is not intended to be invoked by the end user.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.