Description Details Author(s) References See Also Examples

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.

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:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
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.

Charles Doss

Maintainer: 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 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 the package
`logcondens`

, from which
this package derives much of its code.

1 2 3 4 5 6 7 8 | ```
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
``` |

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