| degross.object {degross} | R Documentation |
Object resulting from the estimation of a density from grouped (tabulated) summary statistics
Description
An object returned by the degross function is a list containing several components resulting from the density estimation procedure.
Value
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 frequenciesn.iat convergence of the EM algorithm.lpost.mj: value of the log-posterior for the observed data based on the big bin frequenciesfreq.j.llik.ni: log-likelihood for the complete data based on the estimated small bin frequenciesn.i.llik.mj: log-likelihood for the observed data based on the big bin frequenciesfreq.j.moments.penalty: log of the joint (asymptotic) density for the observed sample moments.penalty: \log p(\phi|\tau) + \log p(\tau).Score&Score.mj: score (w.r.t.\phi) of the log of the observed joint posterior function.Score.ni: score (w.r.t.\phi) of the log-posterior for the complete data based on the expected small bin frequenciesn.iat convergence of the EM algorithm.Fisher&Fisher.ni: information matrix (w.r.t.\phi) based on the log-posterior for the complete data based on the expected small bin frequenciesn.iat convergence of the EM algorithm.Fisher.mj: information matrix (w.r.t.\phi) 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\tau(tau0iffixed.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 ofp(\hat{\phi}_\tau,\hat{\tau} | D)|\Sigma_\phi|^{(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.
Author(s)
Philippe Lambert p.lambert@uliege.be
References
Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.
See Also
degross, print.degross, plot.degross.