degrossData.object {degross}

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.

Description

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.

Value

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.

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.

See Also

degrossData, print.degrossData