robust {logcondens}R Documentation

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 {x}, where w_1 > 0 and w_m > 0. These raw weights are normalized in order to sum to one. Default: w_i = 1/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).

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.staff.unibe.ch/duembgen

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.


[Package logcondens version 1.3.3 Index]