| scores {kergp} | R Documentation |
Generic Function: Scores for a Covariance Kernel Object
Description
Generic function returning the scores for a covariance kernel object.
Usage
scores(object, ...)
Arguments
object |
A covariance object. |
... |
Other arguments passed to methods. |
Details
Compute the derivatives \partial_{\theta_k}\ell
for the (possibly concentrated) log-likelihood \ell :=
\log L of a covariance object with parameter vector
\boldsymbol{\theta}. The score for
\theta_k is obtained as a matrix scalar product
\partial_{\theta_k} \ell
= \textrm{trace}(\mathbf{W} \mathbf{D})
where \mathbf{D} := \partial_{\theta_k} \mathbf{C}
and where \mathbf{W} is the matrix
\mathbf{W} := \mathbf{e}\mathbf{e}^\top - \mathbf{C}^{-1}
.
The vector \mathbf{e} is the vector of residuals
and the matrix \mathbf{C}
is the covariance computed for the design \mathbf{X}.
Value
A numeric vector of length npar(object) containing the scores.
Note
The scores can be efficiently computed when the matrix
\mathbf{W} has already been pre-computed.