robust {logcondens}

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).

Note

This function is not intended to be invoked by the end user.

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

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 https://slsp-ube.primo.exlibrisgroup.com/permalink/41SLSP_UBE/17e6d97/alma99116730175505511.

Rufibach, K. (2007) Computing maximum likelihood estimators of a log-concave density function. J. Stat. Comput. Simul. 77, 561–574.