degross.object: Object resulting from the estimation of a density from...
In degross: Density Estimation from GROuped Summary Statistics

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.