EL.smooth {EL}

Smooth estimates and confidence intervals (or simultaneous bands) using the smoothed two-sample EL method

Description

Calculates estimates and pointwise confidence intervals (or simultaneous bands) for P-P and Q-Q plots, ROC curves, quantile differences (qdiff) and CDF differences (ddiff) using the smoothed empirical likelihood method.

Usage

EL.smooth(method, X, Y, t, bw = bw.nrd0,
          conf.level = NULL, simultaneous = FALSE,
          bootstrap.samples = 300, more.warnings = FALSE)

Arguments

method

"pp", "qq", "roc", "qdiff" or "ddiff".

X

a vector of data values.

Y

a vector of data values.

t

a vector of points for which to calculate the estimates and confidence intervals.

conf.level

confidence level for the intervals. A number between 0 and 1 or NULL when no confidence bands should be calculated. Depending on the value of 'simultaneous' either pointwise intervals or simultaneous confidence bands will be calculated.

simultaneous

if this is TRUE, simultaneous confidence bands will be constructed, using a nonparametric bootstrap procedure to select the level of confidence bands. The default is FALSE, in which case simple pointwise confidence bands are calculated.

bootstrap.samples

the number of samples used to bootstrap the simultaneous confidence bands when 'simultaneous = TRUE'.

bw

a function taking a vector of values and returning the corresponding bandwidth or a vector of two values corresponding to the respective bandwidths of X and Y.

more.warnings

if this is FALSE (the default) a single warning will be produced if there is any problem calculating the estimate or the confidence bands. If this is set to TRUE a warning will be produced for every point at which there was a problem.

Details

Confidence bands are drawn only if 'conf.level' is not 'NULL'.

When constructing simultaneous confidence bands, it is advisable to check whether the chosen range of 't' values does not produce too large bands (for example, for the P-P plot in the example below the interval [0.05, 0.95] was a sensible choice). This has to be checked for each data sample separately by hand. Note that the calculation of simultaneous confidence bands can take a long time.

Value

estimate

the estimated values at points 't'.

conf.int

a two column matrix where each row represents the lower and upper bounds of the confidence bands corresponding to the values at points 't'.

simultaneous.conf.int

will be a true value if simultaneous confidence bands are constructed.

bootstrap.crit

the critical value from the bootstrapped -2 * log-likelihood statistic for simultaneous confidence bands using the confidence level 'conf.level'. Only calculated when 'conf.level' is not NULL and 'simultaneous' is TRUE.

Author(s)

E. Cers, J. Valeinis

References

J. Valeinis and E. Cers. Extending the two-sample empirical likelihood. To be published. Preprint available at http://home.lanet.lv/~valeinis/lv/petnieciba/EL_TwoSample_2011.pdf

P. Hall and A. Owen (1993). Empirical likelihood bands in density estimation. Journal of Computational and Graphical statistics, 2(3), 273-289.

See Also

EL.plot EL.statistic

Examples

#### Simultaneous confidence bands for a P-P plot
X1 <- rnorm(200)
X2 <- rnorm(200, 1)

x <- seq(0.05, 0.95, length=19)
y <- EL.smooth("pp", X1, X2, x, conf.level=0.95,
               simultaneous=TRUE, bw=c(0.3, 0.3))

## Plot the graph with both pointwise and simultaneous confidence bands
EL.plot("pp", X1, X2, conf.level=0.95, bw=c(0.3, 0.3))
lines(x, y$conf.int[1,], lty="dotted")
lines(x, y$conf.int[2,], lty="dotted")