Performs robustification and Hermite interpolation in the iterative convex minorant algorithm as described in Rufibach (2006, 2007).
robust(x, w, eta, etanew, grad)Vector of independent and identically distributed numbers, with strictly increasing entries.
Optional vector of nonnegative weights corresponding to \({\bold{x}_m}\).
Current candidate vector.
New candidate vector.
Gradient of L at current candidate vector \(\eta.\)
Returns a (possibly) new vector \(\eta\) on the segment
$$(1 - t_0) \eta + t_0 \eta_{new} $$
such that the log-likelihood of this new \(\eta\) is strictly greater than that of the initial \(\eta\) and \(t_0\) is chosen according to the Hermite interpolation procedure described in Rufibach (2006, 2007).
Rufibach K. (2006) Log-concave Density Estimation and Bump Hunting for i.i.d. Observations. PhD Thesis, University of Bern, Switzerland and Georg-August University of Goettingen, Germany, 2006. Available at http://www.zb.unibe.ch/download/eldiss/06rufibach_k.pdf.
Rufibach, K. (2007) Computing maximum likelihood estimators of a log-concave density function. J. Stat. Comput. Simul. 77, 561--574.