Calculating the log likelihood

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Description

Calculating the considered log likelihood. If one chooses lambda0=0, one gets the (actual) unpenalized log likelihood. Otherwise, one gets the penalized log likelihood for the used fitted values of the response y and the actual parameter set beta.

Usage

1
pen.log.like(penden.env,lambda0,f.hat.val=NULL,beta.val=NULL)

Arguments

penden.env

Containing all information, environment of pendensity()

lambda0

penalty parameter lambda

f.hat.val

matrix contains the fitted values of the response, if NULL the matrix is caught in the environment

beta.val

actual parameter set beta, if NULL the vector is caught in the environment

Details

The calculation depends on the fitted values of the response as well as on the penalty parameter lambda and the penalty matrix Dm.

\eqn{l(β)=sum(log(sum(c_k(x_i,β) φ_k(y_i))))-0.5*λ β^T D_m β}

.

The needed values are saved in the environment.

Value

Returns the log likelihood depending on the penalty parameter lambda.

Author(s)

Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

References

Density Estimation with a Penalized Mixture Approach, Schellhase C. and Kauermann G. (2012), Computational Statistics 27 (4), p. 757-777.

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