LCLRCImode: Compute Log-Concave Likelihood-Ratio Confidence interval for...
In logcondens.mode: Compute MLE of Log-Concave Density on R with Fixed Mode, and Perform Inference for the Mode.

Description Usage Arguments Details Value Author(s) References See Also Examples

Compute the confidence interval (CI) for the mode of a log-concave density by "inverting" the likelihood ratio statistic, i.e. the 1-α CI is composed of mode values at which the likelihood ratio test does not reject at the α-level.

1 2	LCLRCImode(x, xgrid = NULL, w = NA, nn = length(x), alpha = 0.05, prec = 1e-10, CIprec = 1e-04, print = F)

`x`	Points at which to compute the unconstrained and constrained estimators. Either iid data observations (from a log-concave density) or, such data binned. If `x` is binned, there should be corresponding weights `w`. Binning is usually handled by passing in a non-`NULL` value for `xgrid`.
`xgrid`	Governs binning of `x` and generation of corresponding weights `w`. See `logcondens::preProcess`. If `w` is not `NA` then `xgrid` should be `NULL`.
`w`	Numeric vector of length `length(x)` or `NA`. Weights corresponding to `x`. Can be `NA` (regardless of the value of `xgrid`) which indicates the weights are uniform (equal to `1/length(x)`). If `w` is not `NA` then `xgrid` should be `NULL`. If `nn` is not equal to `length(x)` then `w` should be given a non-`NA` value. If `w` is not `NA`, then we assume that `x` has no duplicate entries.
`nn`	The number of data points initially observed. Numeric of length 1. Usually equal to `length(x)`. If some sort of `preProcess`ing is done in advance, may be not equal to `length(x)`. To pass in a non-default value for `nn` (i.e. something other than `length(x)`), `w` must also be passed in a (numeric vector) value, and `xgrid` must be `NULL`.
`alpha`	Numeric value in `[0,1]`, the coverage probability for the confidence interval (i.e., the level for the corresponding test).
`prec`	Numeric value, giving the precision passed to `activeSetLogCon` and to `activeSetLogCon.mode`.
`CIprec`	Numeric value giving precision for the endpoints of the confidence interval.
`print`	`TRUE` or `FALSE`, depending on whether debugging information should be printed or not, respectively.

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 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 LRmodeTest for the corresponding test.

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

LCLRCImode(x=myxx,
           xgrid=NULL,
           w=NA,
           ##nn=nn, 
           alpha=0.05,
           CIprec=1e-04,
           print=FALSE)

LCLRCImode(x=myxx,
           xgrid=.05,
           w=NA,
           ##nn=nn, 
           alpha=0.05,
           CIprec=1e-04,
           print=FALSE)