EL.plot {EL}

Draws plots using the smoothed two-sample empirical likelihood method

Description

Draws P-P and Q-Q plots, ROC curves, quantile differences (qdiff) and CDF differences (ddiff) and their respective confidence bands (pointwise or simultaneous) using the empirical likelihood method.

Usage

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

Arguments

method

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

X

a vector of data values.

Y

a vector of data values.

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.

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 drawn.

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'.

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.

...

further arguments passed to plot.

Details

The plotting interval for P-P plots, ROC curves and differences of quantile functions is [0, 1] (where these functions are defined). The Q-Q plot is drawn from the minimum to the maximum of 'Y'. Finally, for the plot of distribution function differences the interval from max(min(X), min(Y)) to min(max(X), max(Y)) is used.

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

When constructing simultaneous confidence bands, the plot is drawn on an interval that is narrowed by 5% on both sides, since the procedure is usually sensitive at the end-points, which can result in large bands. The confidence level for the simultaneous confidence bands is bootstrapped using 50 evenly spaced points in this interval. If the default interval produces too large confidence bands, use the function 'EL.smooth' where the intervals are specified manually. Note that calculation of simultaneous confidence bands can take a long time.

Value

none.

Author(s)

E. Cers, J. Valeinis

References

J. Valeinis, 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.smooth EL.statistic

Examples

## The examples showcase all available graphs

X1 <- rchisq(100, 2.5)
X2 <- rnorm(100, 0, 1)


p <- par(lwd=2, mfrow=c(3,2))

# Intro
xlim <- c(min(X1, X2) - 0.5, max(X1, X2) + 0.5)
D1 <- density(X1)
D2 <- density(X2)
ylim <- c(min(D1$y, D2$y), max(D1$y, D2$y))
plot(D1, xlim=xlim, ylim=ylim, main="Distribution functions", xlab="x")
lines(D2, lty="dashed")
legend("topright", c(eval(substitute(expression(paste("X1 (bw = ", a, ")")),
                                     list(a = round(D1$bw, 2)))),
                     eval(substitute(expression(paste("X2 (bw = ", a, ")")),
                                     list(a = round(D2$bw, 2))))),
                   lty=c("solid", "dashed"))

# CDF differences
EL.plot("fdiff", X1, X2, main="F difference", conf.level=0.95)
tt <- seq(max(c(min(X1), min(X2))), min(c(max(X1), max(X2))), length=30)
ee <- ecdf(X2)(tt) - ecdf(X1)(tt)
points(tt, ee)

# Quantile differences
EL.plot("qdiff", X1, X2, main="Quantile difference", conf.level = 0.95)
tt <- seq(0.01, 0.99, length=30)
ee <- quantile(X2, tt) - quantile(X1, tt)
points(tt, ee)

# Q-Q plot
EL.plot("qq", X1, X2, main="Q-Q plot", conf.level=0.95)
tt <- seq(min(X2), max(X2), length=30)
ee <- quantile(X1, ecdf(X2)(tt))
points(tt, ee)

# P-P plot
EL.plot("pp", X1, X2, main="P-P plot", conf.level=0.95, ylim=c(0,1))
tt <- seq(0.01, 0.99, length=30)
ee <- ecdf(X1)(quantile(X2, tt))
points(tt, ee)


# ROC curve
EL.plot("roc", X1, X2, main="ROC curve", conf.level=0.95, ylim=c(0,1))
tt <- seq(0.01, 0.99, length=30)
ee <- 1- ecdf(X1)(quantile(X2, 1-tt))
points(tt, ee)

par(p)