| new.beta.val {pendensity} | R Documentation |
Calculating the new parameter beta
Description
Calculating the direction of the Newton-Raphson step for the known beta and iterate a step size bisection to control the maximizing of the penalized likelihood.
Usage
new.beta.val(llold, penden.env)
Arguments
llold |
log likelihood of the algorithm one step before |
penden.env |
Containing all information, environment of pendensity() |
Details
We terminate the search for the new beta, when the new log likelihood is smaller than the old likelihood and the step size is smaller or equal 1e-3. We calculate the direction of the Newton Raphson step for the known beta_t and iterate a step size bisection to control the maximizing of the penalized likelihood
l_p(\beta_t,\lambda_0)
. This means we set
\beta_{t+1}=\beta_t - 2^{-v} \{s_p(\beta_t,\lambda_0) \cdot (-J_p(\beta_t,\lambda_0))^{-1}\}
with s_p as penalized first order derivative and J_p as penalized second order derivative. We begin with v=0. Not yielding a new maximum for a current v, we increase v step by step respectively bisect the step size. We terminate the iteration, if the step size is smaller than some reference value epsilon (eps=1e-3) without yielding a new maximum. We iterate for new parameter beta until the new log likelihood depending on the new estimated parameter beta differ less than 0.1 log-likelihood points from the log likelihood estimated before.
Value
Likelie |
corresponding log likelihood |
step |
used step size |
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.