Description Usage Arguments Details Value Author(s) References See Also Examples
Compute the confidence interval (CI) for the mode of a logconcave density by "inverting" the likelihood ratio statistic, i.e. the 1α CI is composed of mode values at which the likelihood ratio test does not reject at the αlevel.
1 2  LCLRCImode(x, xgrid = NULL, w = NA, nn = length(x), alpha = 0.05, prec =
1e10, CIprec = 1e04, print = F)

x 
Points at which to compute the unconstrained and constrained
estimators. Either iid data observations (from a logconcave
density) or, such data binned. If 
xgrid 
Governs binning of 
w 
Numeric vector of length 
nn 
The number of data points initially observed. Numeric of length
1. Usually equal to 
alpha 
Numeric value in 
prec 
Numeric value, giving the precision passed to

CIprec 
Numeric value giving precision for the endpoints of the confidence interval. 
print 

The confidence set is given by the values of the mode that
LRmodeTest
does not reject. See the details of that
function.
Returns a numeric vector of length 2, giving the asymptotic confidence interval for the mode location.
Charles R. 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 logconcave 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 logconcave 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 LogConcave Density Estimation. Journal of Statistical Software, 39(6), 1–28. http://www.jstatsoft.org/v39/i06
Doss, C. R. (2013). ShapeConstrained Inference for ConcaveTransformed 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 logconcave density. Technical Report, University of Washington, in preparation.
See also LRmodeTest
for the corresponding test.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  nn < 200
myxx < rnorm(nn) ## no need to sort
LCLRCImode(x=myxx,
xgrid=NULL,
w=NA,
##nn=nn,
alpha=0.05,
CIprec=1e04,
print=FALSE)
LCLRCImode(x=myxx,
xgrid=.05,
w=NA,
##nn=nn,
alpha=0.05,
CIprec=1e04,
print=FALSE)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.