mkle.ci {MKLE}

Confidence intervals for the maximum kernel likelihood estimator

Description

Computes different confidence intervals for the maximum kernel likelihood estimator for a given dataset and bandwidth.

Usage

mkle.ci(data, bw=2*sd(data), alpha=0.1, kernel=c("gaussian", "epanechnikov", 
        "rectangular", "triangular", "biweight", "cosine", "optcosine"), 
        method=c("percentile", "wald","boott"), B=1000, gridsize=2^14)

Arguments

data

the data for which the confidence interval should be found.

bw

the smoothing bandwidth to be used.

alpha

the significance level.

kernel

a character string giving the smoothing kernel to be used. This must be one of '"gaussian"', '"rectangular"', '"triangular"', '"epanechnikov"', '"biweight"', '"cosine"' or '"optcosine"', with default '"gaussian"', and may be abbreviated to a unique prefix (single letter).

method

a character string giving the type of interval to be used. This must be one of '"percentile"', '"wald"' or '"boott"'.

B

number of resamples used to estimate the mean squared error with 1000 as the default.

gridsize

the number of points at which the kernel density estimator is to be evaluated with 2^{14} as the default.

Details

The method can be a vector of strings containing the possible choices.

The bootstrap-t-interval can be very slow for large datasets and a large number of resamples as a two layered resampling is necessary.

Value

A dataframe with the requested intervals.

Author(s)

Thomas Jaki

References

Jaki T., West R. W. (2008) Maximum kernel likelihood estimation. Journal of Computational and Graphical Statistics Vol. 17(No 4), 976-993.

Davison, A. C. and Hinkley, D. V. (1997), Bootstrap Methods and their Applications, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press.

See Also

mkle

Examples

data(state)
mkle.ci(state$CRIME,method=c('wald','percentile'),B=100,gridsize=2^11)