1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
|
## Demo of nonlinear quantile regression model based on Frank copula
vFrank <- function(x, df, delta, u)
-log(1-(1-exp(-delta))/(1+exp(-delta*pt(x,df))*((1/u)-1)))/delta
FrankModel <- function(x, delta, mu,sigma, df, tau) {
z <- qt(vFrank(x, df, delta, u = tau), df)
mu + sigma*z
}
n <- 200
df <- 8
delta <- 8
set.seed(1989)
x <- sort(rt(n,df))
v <- vFrank(x, df, delta, u = runif(n))
y <- qt(v, df)
plot(x, y, pch="o", col="blue", cex = .25)
Dat <- data.frame(x = x, y = y)
us <- c(.25,.5,.75)
for(i in 1:length(us)){
v <- vFrank(x, df, delta, u = us[i])
lines(x, qt(v,df))
}
cfMat <- matrix(0, 3, length(us))
trace <- TRUE # a bit noisy ...
trace <- FALSE
for(i in 1:length(us)) {
tau <- us[i]
cat("tau = ", format(tau), ".. ")
fit <- nlrq(y ~ FrankModel(x, delta,mu,sigma, df = 8, tau = tau),
data = Dat, tau = tau,
start= list(delta=5, mu = 0, sigma = 1),
trace = trace)
lines(x, predict(fit, newdata=x), lty=2, col="red")
cfMat[i,] <- coef(fit)
cat("\n")
}
colnames(cfMat) <- names(coef(fit))
cfMat
|
