logcondens.mode (version 1.0.1)

logcondens.mode-package: Computation of Log-Concave Densities on R with fixed mode and Inference for the Mode.

Description

Extension of the logcondens package. Computes maximum likelihood estimate of a log-concave density with fixed and known location of the mode. Performs inference about the mode via a likelihood ratio test comparing the unconstrained log-concave estimator to the constrained one.

Details

Package:

logcondens.mode

Type:

Package

Version:

1.0

Date:

2013-05-24

License:

GPL (>= 2)

Depends:

logcondens

Imports:

distr

Suggests:

distr

LazyLoad:

yes

Packaged:

2013-07-10 07:59:40 UTC; cdoss

Built:

R 2.15.2; ; 2013-07-10 07:59:41 UTC; unix

Index:

LCLRCImode              Compute Log-Concave Likelihood-Ratio Confidence
                        interval for the mode.
LRmodeTest              Computes an Asymptotic Confidence Interval for
                        the mode of a Log-Concave Density
LocalExtend             Auxiliary Numerical Routine for the Function
                        activeSetLogCon.mode
activeSetLogCon         Computes a Log-Concave Probability Density
                        Estimate via an Active Set Algorithm
activeSetLogCon.mode    Computes the Modally-Constrained Log-Concave
                        Probability Density Maximum Likelihood Estimate
                        via an Active Set Algorithm.
dir.exists              Utility for checking existence of a directory.
estimateLRdistn         Estimate "the" limiting distribution of the
                        likelihood ratio statistic for location of
                        mode.
intECDFfn               Gives the Integrated Empirical Distribution
                        Function
intF                    Computes the Integral of the estimated CDF at
                        Arbitrary Real Numbers in s
intFfn                  Computes the Integral of a log-concave CDF at
                        Arbitrary Real Numbers
logConDens              Compute log-concave density estimator and
                        related quantities
                      

The main functions of this package are LCLRCImode, LRmodeTest, and activeSetLogCon.mode. The latter computes a log-concave density estimate with known and fixed location of the mode. In addition to being of interest on its own, this estimator is of interest for likelihood ratio tests for the mode. LRmodeTest runs this test by using activeSetLogCon and activeSetLogCon.mode to compute the likelihood ratio statistic and LCTLLRdistn to compute the quantiles. LCLRCImode inverts the test to form confidence intervals.

References

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.

See Also

See the package logcondens, from which this package derives much of its code.

Examples

nn <- 200
myxx <- rnorm(nn) ## no need to sort
TRUEMODE <- 0

res.MC <- activeSetLogCon.mode(myxx, mode=TRUEMODE)
LRmodeTest(mode=TRUEMODE, x=myxx, xgrid=.05, alpha=.05)
CI <- LCLRCImode(x=myxx, alpha=0.05)
print(CI[1] <= TRUEMODE && TRUEMODE <= CI[2]) ## approx 95% coverage probability