Robustification and Hermite Interpolation for ICMA
Performs robustification and Hermite interpolation in the iterative convex minorant algorithm as described in Rufibach (2006, 2007).
robust(x, w, eta, etanew, grad)
x |
Vector of independent and identically distributed numbers, with strictly increasing entries. |
w |
Optional vector of nonnegative weights corresponding to x_m. |
eta |
Current candidate vector. |
etanew |
New candidate vector. |
grad |
Gradient of L at current candidate vector η. |
Returns a (possibly) new vector η on the segment
(1 - t_0) η + t_0 η_{new}
such that the log-likelihood of this new η is strictly greater than that of the initial η and t_0 is chosen according to the Hermite interpolation procedure described in Rufibach (2006, 2007).
This function is not intended to be invoked by the end user.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
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.
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