Calculating the AIC value of the density estimation. Therefore, we add the unpenalized log likelihood of the estimation and the degree of freedom, which are
my.AIC(penden.env, lambda0, opt.Likelihood = NULL)Containing all information, environment of pendensity()
penalty parameter lambda
optimal unpenalized likelihood of the density estimation
sum of the negative unpenalized log likelihood and mytrace
calculated mytrace as the sum of the diagonal matrix df, which results as the product of the inverse of the penalized second order derivative of the log likelihood with the unpenalized second order derivative of the log likelihood
AIC is calculated as \(AIC(\lambda)= - l(\hat{\beta}) + df(\lambda)\)
Density Estimation with a Penalized Mixture Approach, Schellhase C. and Kauermann G. (2012), Computational Statistics 27 (4), p. 757-777.