Obtains Bayesian parameter covariance matrix, frequentist
parameter estimator covariance matrix, estimated degrees of
freedom for each parameter and leading diagonal of influence/hat matrix,
for a penalized regression estimated by `magic`

.

1 | ```
magic.post.proc(X,object,w=NULL)
``` |

`X` |
is the model matrix. |

`object` |
is the list returned by |

`w` |
is the weight vector used in fitting, or the weight matrix used
in fitting (i.e. supplied to |

`object`

contains `rV`

(*V*, say), and
`scale`

(*s*, say) which can be
used to obtain the require quantities as follows. The Bayesian covariance matrix of
the parameters is *VV's*. The vector of
estimated degrees of freedom for each parameter is the leading diagonal of
* VV'X'W'WX*
where *W* is either the
weight matrix `w`

or the matrix `diag(w)`

. The
hat/influence matrix is given by
* WXVV'X'W'*
.

The frequentist parameter estimator covariance matrix is
* VV'X'W'WXVV's*:
it is sometimes useful for testing terms for equality to zero.

A list with three items:

`Vb` |
the Bayesian covariance matrix of the model parameters. |

`Ve` |
the frequentist covariance matrix for the parameter estimators. |

`hat` |
the leading diagonal of the hat (influence) matrix. |

`edf` |
the array giving the estimated degrees of freedom associated with each parameter. |

Simon N. Wood simon.wood@r-project.org

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