R: Gradient and Diagonal of Hesse Matrix of Quadratic...
Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L
Description
Computes gradient and diagonal of the Hesse matrix w.r.t. to η of a quadratic approximation to the
reparametrized original log-likelihood function
L(φ) = ∑_{i=1}^m w_i φ(x_i) - int_{-∞}^{∞} exp(φ(t)) dt.
where L is parametrized via
η(φ) = (φ_1, (η_1 + ∑_{j=2}^i (x_i-x_{i-1}) η_i)_{i=2}^m).
φ: vector (φ(x_i))_{i=1}^m representing concave, piecewise linear function φ, η: vector representing successive slopes of φ.
Usage
quadDeriv(dx, w, eta)
Arguments
dx |
Vector (0, x_i-x_{i-1})_{i=2}^m.
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w |
Vector of weights as in activeSetLogCon .
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eta |
Vector η.
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Value
m \times 2 matrix. First column contains gradient and second column diagonal of Hesse matrix.
Note
This function is not intended to be invoked by the end user.
Author(s)
Kaspar Rufibach, kaspar.rufibach@gmail.com, http://www.kasparrufibach.ch
Lutz Duembgen, duembgen@stat.unibe.ch, http://www.stat.unibe.ch/content/staff/personalhomepages/duembgen/index_eng.html
See Also
quadDeriv is used by the function icmaLogCon .
Results
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