Description Author(s) References See Also
Internal functions for the estimation of a log-concave probability mass function. These functions are not intended to be called by the user directly.
Direction
Compute vector that points in direction of \max L(ψ) via Newton step.
dMLE
Compute the vector ψ s.t. the log-likelihood function L, as implemented in LikFunk
, is maximized
over all PMFs (under no additional restrictions, though).
GradientL
Gradient of LikFunk
.
HesseL
Hesse matrix of LikFunk
.
J00
Function introduced in Section 2.3 in Weyermann (2007), defined as
J^{δ_k}(ψ_k, ψ_{k+1}) := ∑_{j=0}^{δ_k} \exp \Bigl((1-j/δ_k)ψ_k + (j/δ_k) ψ_{k+1} \Bigr).
This function is used to compute the value of the log-likelihood in LikFunk
.
J10
Derivative of J^{δ_k}(ψ_k, ψ_{k+1}) w.r.t to the first argument.
J11
Derivative of J^{δ_k}(ψ_k, ψ_{k+1}) w.r.t to both arguments.
J20
Second derivative of J^{δ_k}(ψ_k, ψ_{k+1}) w.r.t to the first argument.
LikFunk
The log-likelihood function for the discrete log-concave MLE.
LocalCoarsen
Auxiliary function.
LocalConcavity
Auxiliary function.
LocalExtend
Auxiliary function.
LocalMLE
Auxiliary function.
LocalNormalize
Auxiliary function.
StepSize
Auxiliary function.
Kaspar Rufibach (maintainer) kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch
Fadoua Balabdaoui fadoua@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~fadoua
Hanna Jankowski hkj@mathstat.yorku.ca
http://www.math.yorku.ca/~hkj
Kathrin Weyermann
Balabdaoui, F., Jankowski, H., Rufibach, K., and Pavlides, M. (2013). Maximum likelihood estimation and confidence bands for a discrete log-concave distribution. J. R. Stat. Soc. Ser. B Stat. Methodol., 75(4), 769–790.
Weyermann, K. (2007). An Active Set Algorithm for Log-Concave Discrete Distributions. MSc thesis, University of Bern (Supervisor: Lutz Duembgen).
All these functions are used by the function logConDiscrMLE
.
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