dlcd {LogConcDEAD} | R Documentation |
This function evaluates the density function of a log-concave maximum likelihood estimator at a point or points.
dlcd(x,lcd, uselog=FALSE) lcd.eval(lcd, po, uselog=FALSE)
x, po |
Point (or matrix of points) at which the maximum
likelihood estimator should be evaluated |
lcd |
Object of class "LogConcDEAD" (typically output from
mlelcd ) |
uselog |
Scalar logical : should the estimator should be calculated on the
log scale? |
A log-concave maximum likelihood estimate f_n is satisfies log f_n = h_y for some y in R^n, where
h_y(x) = inf{h(x): h concave, h(x_i) >= y_i for i = 1, ..., n}.
Functions of this form may equivalently be specified by dividing C_n, the convex hull of the data into simplices C_j for j in J (triangles in 2d, tetrahedra in 3d etc), and setting
f(x) = exp{b_j^T x - beta_j}
for x in C_j, and f(x) = 0 for x not in C_n. The estimated density is zero outside the convex hull of the data.
The estimate may therefore be evaluated by finding the appropriate simplex C_j, then evaluating f(x) = exp{b_j^T x - beta_j} (if x not in C_n, set f(x) = 0).
For examples, see mlelcd
.
lcd.eval
is deprecated, but retained for compatibility with
previous versions.
A vector
of maximum likelihood estimate (or log
maximum likelihood estimate) values, as evaluated at the points x
.
Madeleine Cule mlc40@cam.ac.uk
Robert Gramacy
Richard Samworth