Description Usage Arguments Details Value Author(s) References
View source: R/penalty.matrix.R
Calculating the penalty matrix P depends on the number of covariates 'p', the order of differences to be penalized 'pen.order', the number of observations 'n' and the penalty parameters 'lambda”.
1 | penalty.matrix(penden.env, temp = FALSE)
|
penden.env |
Containing all information, environment of pencopula(). |
temp |
If TRUE, the iteration for a new 'b' is not finished and a temporary penalty matrix is calculated, default = FALSE. |
The penalty matrix is calculated as
P(λ)=∑_{j=1}^{p} λ_j P_j
with
P_j=≤ft(\bigotimes_{l=1}^{j-1}{I}\right) \otimes \{({A^{-1})^T} P {A}^{-1}\} \otimes ≤ft(\bigotimes_{l=j+1}^p {I}\right)
The needed values are calculated or saved in the environment 'penden.env'.
There is no penalty used for the Bernstein polynomial basis, P=0.
DDD.sum |
Penalty matrix P |
Matrix is saved in the environment.
Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
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