Description Value Author(s) References See Also
An object returned by the degross
function is a list containing several components resulting from the density estimation procedure.
A degross
object is a list containing, after convergence of the EM algorithm :
lpost
& lpost.ni
:
value of the log-posterior for the complete data based on the expected small bin frequencies n.i
at convergence of the EM algorithm.
lpost.mj
:
value of the log-posterior for the observed data based on the big bin frequencies freq.j
.
llik.ni
:
log-likelihood for the complete data based on the estimated small bin frequencies n.i
.
llik.mj
:
log-likelihood for the observed data based on the big bin frequencies freq.j
.
moments.penalty
:
log of the joint (asymptotic) density for the observed sample moments.
penalty
:
\log p(φ|τ) + \log p(τ).
Score
& Score.mj
:
score (w.r.t. φ) of the log of the observed joint posterior function.
Score.ni
:
score (w.r.t. φ) of the log-posterior for the complete data based on the expected small bin frequencies n.i
at convergence of the EM algorithm.
Fisher
& Fisher.ni
:
information matrix (w.r.t. φ) based on the log-posterior for the complete data based on the expected small bin frequencies n.i
at convergence of the EM algorithm.
Fisher.mj
:
information matrix (w.r.t. φ) based on the log of the observed joint posterior function.
M.j
:
theoretical moments of the fitted density within a big bin.
pi.i
:
small bin probabilities (at convergence).
ui
:
small bin midpoints.
delta
:
width of the small bins.
gamma.j
:
big bin probabilities (at convergence).
tau
:
value of the roughness penalty parameter τ (tau0
if fixed.tau
=TRUE, estimated otherwise).
phi
:
vector with the spline parameters (at convergence).
n.i
:
small bin frequencies under the estimated density (at convergence).
edf
:
the effective degrees of freedom (or effective number of spline parameters) (at convergence).
aic
:
-2*(llik.mj
+ moments.penalty
) + 2edf
.
bic
:
-2(llik.mj
+ moments.penalty
) + \log(n)*edf
.
log.evidence
:
approximation to the log of p(\hat{φ}_τ,\hat{τ} | D) |Σ_φ|^{(1/2)}.
degross.data
:
the degrossData object from which density estimation proceeded.
use.moments
:
vector of 4 logicals indicating which tabulated sample moments were used as soft constraints during estimation.
diag.only
:
logical indicating whether the off-diagonal elements of the variance-covariance matrix of the sample central moments were ignored. Default: FALSE.
logNormCst
:
log of the normalizing constant when evaluating the density.
Philippe Lambert p.lambert@uliege.be
Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.
degross
, print.degross
, plot.degross
.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.