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degross (version 0.9.0)

Density Estimation from GROuped Summary Statistics

Description

Estimation of a density from grouped (tabulated) summary statistics evaluated in each of the big bins (or classes) partitioning the support of the variable. These statistics include class frequencies and central moments of order one up to four. The log-density is modelled using a linear combination of penalised B-splines. The multinomial log-likelihood involving the frequencies adds up to a roughness penalty based on the differences in the coefficients of neighbouring B-splines and the log of a root-n approximation of the sampling density of the observed vector of central moments in each class. The so-obtained penalized log-likelihood is maximized using the EM algorithm to get an estimate of the spline parameters and, consequently, of the variable density and related quantities such as quantiles, see Lambert, P. (2021) for details.

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Version

Install

install.packages('degross')

Monthly Downloads

210

Version

0.9.0

License

GPL-3

Maintainer

Philippe Lambert

Last Published

August 4th, 2021

Functions in degross (0.9.0)

Log-posterior (with gradient and Fisher information) for given spline parameters, small bin frequencies, tabulated sample moments and roughness penalty parameter. This function is maximized during the M-step of the EM algorithm to estimate the B-spline parameters entering the density specification.

Density estimation from tabulated data with given frequencies and group central moments.

Cumulative distribution function (cdf) based on an object resulting from the estimation procedure in degross.

Creates a degrossData.object from the observed tabulated frequencies and central moments.

degross_lpostBasic

Log-posterior for given spline parameters, big bin (and optional: small bin) frequencies, tabulated sample moments and roughness penalty parameter. Compared to degross_lpost, no Fisher information matrix is computed and the gradient evaluation is optional, with a resulting computational gain.

Object resulting from the estimation of a density from grouped (tabulated) summary statistics

Plot the density estimate obtained from grouped summary statistics using degross and superpose it to the observed histogram.

Density function based on an object resulting from the estimation procedure in degross.

Variance-covariance of sample central moments (root-n approximation) given the vector mu with the theoretical moments of order 1 to 8. CAREFUL: the result must be divided by n (= sample size)!

degrossData.object

Object generated from grouped summary statistics, including tabulated frequencies and central moments of order 1 up to 4, to estimate the underlying density using degross.

Print a 'degross' object.

print.degrossData

Print a 'degrossData' object.

Simulation of grouped data and their sample moments to illustrate the degross density estimation procedure

Quantile function based on an object resulting from the estimation procedure in degross.