Function that performs the actual fitting of the expert's distribution
via quadratic programming (using the solve.QP function
from the quadprog package). This function is mainly for
internal use.
fit.SEL(N, alpha, P, A, b, gamma, dplus = 0)Returns solution of the quadratic programming problem.
Matrix containing the B-spline basis functions evaluated at the elicited quantiles.
Vector giving the levels of the elicited quantiles.
Penalty matrix (called Omega in the reference below).
Matrix and vector containing the specifying the constraints A'b >= 0.
Gamma parameter trading of goodness of fit and Brier entropy/Brier divergence.
Additional offset for dvec in solve.QP.
Bjoern Bornkamp
Bornkamp, B. and Ickstadt, K. (2009). A Note on B-Splines for Semiparametric Elicitation. The American Statistician, 63, 373--377
Goldfarb, D., and Idnani, A. (1982), Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs, in Numerical Analysis, (eds.) J. Hennart, Springer Verlag, Berlin, pp. 226--239.
Goldfarb, D., and Idnani, A. (1983), A Numerically Stable Dual Method for Solving Strictly Convex Quadratic Programs'', Mathematical Programming, 27, 1--33.
SEL, solve.QP