evaluateLogConDens {logcondens} | R Documentation |
Evaluates the Log-Density MLE and Smoothed Estimator at Arbitrary Real Numbers xs
Description
Based on a "dlc"
object generated by logConDens
, this function computes the values of
\widehat \phi_m(t)
\widehat f_m(t) = \exp(\widehat \phi_m(t))
\widehat F_m(t) = \int_{x_1}^t \exp(\widehat \phi_m(x)) dx
\widehat f_m^*(t) = \exp(\widehat \phi_m^*(t))
\widehat F_m^*(t) = \int_{x_1}^t \exp(\widehat \phi_m^*(x)) dx
at all real number t
in xs
. The exact formula for \widehat F_m
and t \in [x_j,x_{j+1}]
is
\widehat F_m(t) = \widehat F_m(x_j) + (x_{j+1}-x_j) J\Big(\widehat \phi_j, \widehat \phi_{j+1}, \frac{t-x_j}{x_{j+1}-x_j} \Big)
for the function J
introduced in Jfunctions
. Closed formulas can also be given for \widehat f_m^*(t)
and \widehat F_m^*(t)
.
Usage
evaluateLogConDens(xs, res, which = 1:5, gam = NULL, print = FALSE)
Arguments
xs |
Vector of real numbers where the functions should be evaluated at. |
res |
An object of class |
which |
A (sub-)vector of |
gam |
Only necessary if |
print |
Progress in computation of smooth estimates is shown. |
Value
Matrix with rows (x_{0, i}, \widehat \phi_m(x_{0, i}), \widehat f_m(x_{0, i}), \widehat F_m(x_{0, i}), \widehat f_m^*(x_{0, i}), \widehat F_m^*(x_{0, i}))
where x_{0,i}
is the i
-th entry of xs
.
Author(s)
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Lutz Duembgen, duembgen@stat.unibe.ch,
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html
Examples
## estimate gamma density
set.seed(1977)
x <- rgamma(200, 2, 1)
res <- logConDens(x, smoothed = TRUE, print = FALSE)
## compute function values at an arbitrary point
xs <- (res$x[100] + res$x[101]) / 2
evaluateLogConDens(xs, res)
## only compute function values for non-smooth estimates
evaluateLogConDens(xs, res, which = 1:3)