Local_LL_all: Log-likelihood, New Candidate and Directional Derivative for...
In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

Local_LL_all

R Documentation

Log-likelihood, New Candidate and Directional Derivative for L

Computes the value of the log-likelihood function

L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{x_1}^{x_m} \exp(\phi(t)) dt,

a new candidate for \phi via the Newton method as well as the directional derivative of {\bold{\phi}} \to L({\bold{\phi}}) into that direction.

Local_LL_all(x, w, phi)

`x`	Vector of independent and identically distributed numbers, with strictly increasing entries.
`w`	Optional vector of nonnegative weights corresponding to `{\bold{x}_m}`.
`phi`	Some vector `{\bold{\phi}}` of the same length as `{\bold{x}}` and `{\bold{w}}`.

`ll`	Value `L(\phi)` of the log-likelihood function at `\phi.`
`phi_new`	New candidate for `\phi` via the Newton-method, using the complete Hessian matrix.
`dirderiv`	Directional derivative of `\phi \to L(\phi)` into the direction `\phi_{new}.`