degross.An object returned by the degrossData function from tabulated frequencies and central moments of order 1 up to 4. It is used in a second step by degross to estimate the underlying density.
A list containing :
small.bins : a vector of length I+1 with the small bin limits.
ui : the I midpoints of the small bins.
delta : width of the small bins.
I : the number of small bins.
B.i : a matrix of dim I by K with the B-spline basis evaluated at the small bin midpoints.
K : number of B-splines in the basis.
knots : equidistant knots supporting the B-splines basis.
Big.bins : vector of length J+1 with the limits of the J big bins containing the data used to produce the tabulated statistics.
freq.j : the number of data observed within each big bin.
m.j : a matrix of dim J by 4 giving the first 4 sample central moments within each big bin.
J : the number of big bins.
small.to.big : a vector of length I indicating to what big bin each element of ui belongs.
Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.