a)



In [1]:

    
require('MASS')









    



Loading required package: MASS



In [2]:

    
par(mfrow=c(2,2))
hist(geyser$waiting, prob=TRUE, xlab="s", ylab="", main="Waiting + Gaussian + Scott's")
lines(density(geyser$waiting, bw="nrd", kernel="gaussian"))
hist(geyser$waiting, prob=TRUE, xlab="s", ylab="", main="Waiting + Epanechnikov + Scott's")
lines(density(geyser$waiting, bw="nrd", kernel="epanechnikov"))
hist(geyser$waiting, prob=TRUE, xlab="s", ylab="", main="Waiting + Gaussian + BCV")
lines(density(geyser$waiting, bw="ucv", kernel="gaussian"))
hist(geyser$waiting, prob=TRUE, xlab="s", ylab="", main="Waiting + Epanechnikov + UCV")
lines(density(geyser$waiting, bw="ucv", kernel="epanechnikov"))



In [3]:

    
par(mfrow=c(2,2))
hist(geyser$duration, prob=TRUE, xlab="s", ylab="", main="Duration + Gaussian + Scott's")
lines(density(geyser$duration, bw="nrd", kernel="gaussian"))
hist(geyser$duration, prob=TRUE, xlab="s", ylab="", main="Duration + Epanechnikov + Scott's")
lines(density(geyser$duration, bw="nrd", kernel="epanechnikov"))
hist(geyser$duration, prob=TRUE, xlab="s", ylab="", main="Duration + Gaussian + UCV")
lines(density(geyser$duration, bw="bcv", kernel="gaussian"))
hist(geyser$duration, prob=TRUE, xlab="s", ylab="", main="Duration + Epanechnikov + BCV")
lines(density(geyser$duration, bw="bcv", kernel="epanechnikov"))

b)



In [4]:

    
COL <- gray(30:100 /100)



In [5]:

    
old.par <- par(mfrow=c(2,2))
plot(geyser$waiting, geyser$duration, xlab="waiting", ylab="duration", main="Scatterplot")
f1 <- kde2d(geyser$waiting, geyser$duration, n=50)
image(f1, xlab="waiting", ylab="duration", main="Scott's normal rule", col=COL)
contour(f1, add=TRUE, drawlabels=FALSE)
f2 <- kde2d(geyser$waiting, geyser$duration, n=50, h=c(width.SJ(geyser$waiting), width.SJ(geyser$duration)))
image(f2, xlab="waiting", ylab="duration", main="Sheather-Jones's method", col=COL)
contour(f2, add=TRUE, drawlabels=FALSE)