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logcondens (version 2.1.8)

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)

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).

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 \(\eta.\)

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.