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 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(\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 frequencies`n.i`

at 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 frequencies`n.i`

at 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`

(`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`

) + 2`edf`

.`bic`

:` `

-2(`llik.mj`

+`moments.penalty`

) +`\log(n)`

*`edf`

.`log.evidence`

:` `

approximation to the log of`p(\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`

.

*degross*version 0.9.0 Index]