robust: Robustification and Hermite Interpolation for ICMA
Description
Performs robustification and Hermite interpolation in the iterative convex minorant algorithm as described in Rufibach (2006, 2007).
Usage
robust(x, w, eta, etanew, grad)
Arguments
x
Vector of independent and identically distributed numbers, with strictly increasing entries.
w
Optional vector of nonnegative weights corresponding to ${\bold{x}_m}$.
eta
Current candidate vector.
etanew
New candidate vector.
grad
Gradient of L at current candidate vector $\eta.$
Value
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).
References
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.stub.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.