# NOT RUN {
data(smokerlead)
attach(smokerlead)
w<-rank(abs(llead)) # Wilcoxon ranks
o<-order(w)
brn<-bmhranks(llead) # Brown (1981) ranks
plot(w[o],brn[o],type="n",xlab="Wilcoxon ranks",ylab="Step Ranks",
main="Comparison of 3 Step Ranks")
lines(w[o],brn[o],col="black")
# The following two-step ranks were best for Normal data in
# Table 2 of Markowski-Hettmansperger (1982).
mhn<-bmhranks(llead,q1=.4,q2=.8)
lines(w[o],mhn[o],col="blue")
# Noether (1973) ranks take a single step. The case of a step
# at q1=q2=2/3 was evaluated in Rosenbaum (2015, Table 2).
noe<-bmhranks(llead,q1=2/3,q2=2/3)
lines(w[o],noe[o],col="red")
legend(20,1.75,c("Brown","MH","Noether"),
lty=c(1,1,1),col=c("black","blue","red"))
# Adaptive choice of Brown or Noether ranks was considered in
# Rosenbaum (2012). In this case, an exact distribution
# is available, but function tt() uses a limiting Normal
# distribution instead.
H<-cbind(brn,noe)
tt(llead,H,gamma=1)
tt(llead,H,gamma=3.7)
rm(w,brn,mhn,noe,H)
detach(smokerlead)
# }
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