Description Usage Arguments Value Author(s) References See Also Examples
Based on output from the function logConDens
,
activeSetLogCon
, or activeSetLogCon.mode
,
this function gives a function \widehat I given by
\hat I(l,r) = \int_{l}^{r} \hat{F}(u) du
or by
\hat I(l,r) = \int_{l}^{r} (1-\hat{F}(u)) du
Note that l and r must lie in [x_1,x_m]. For exact formulas
related to these integrals, see the intF
function.
1 | intFfn(x, phi, Fhat, prec = 1e-10, side = "left")
|
x |
Vector of (unique) observations from which the (modally-constrained or
-unconstrained) log-concave density
is estimated. This corresponds to output of
|
phi |
Numeric vector of same length as |
Fhat |
Numeric vector of same length as |
prec |
Precision argument for the |
side |
String taking values "left" or "right". If "left" then returns the first integral given in the description (integral of \widehat{F}). If "right" then returns the second integral given in the description (integral of 1-\widehat{F}). |
Returns a function H. If side
is "left" then the return is of type
1 |
If side
is "right" then the return is of type
1 |
Note that the order of the arguments are changed, so that passing an unnamed numeric value or vector has a default behavior of integrating "from the outside-in".
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.staff.unibe.ch/duembgen
Charles Doss, cdoss@stat.washington.edu,
http://www.stat.washington.edu/people/cdoss/
Duembgen, L, Huesler, A. and Rufibach, K. (2010) Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at http://arxiv.org/abs/0707.4643.
Duembgen, L. and Rufibach, K. (2009) Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency. Bernoulli, 15(1), 40–68.
Duembgen, L. and Rufibach, K. (2011) logcondens: Computations Related to Univariate Log-Concave Density Estimation. Journal of Statistical Software, 39(6), 1–28. http://www.jstatsoft.org/v39/i06
Doss, C. R. (2013). Shape-Constrained Inference for Concave-Transformed Densities and their Modes. PhD thesis, Department of Statistics, University of Washington, in preparation.
Doss, C. R. and Wellner, J. A. (2013). Inference for the mode of a log-concave density. Technical Report, University of Washington, in preparation.
This function uses the output of activeSetLogCon
or
activeSetLogCon.mode
. The function intECDFfn
is similar, but based on the empirical distribution function. The
function intF
behaves similarly but returns a vector
instead of a function.
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