Figuring out whether logspline density estimation is any good

dlogspline.R

# Figuring out whether this logspline thing is any good
library(logspline)

# mixture
d1 <- function(x) 0.6*dnorm(x) + 0.3*dlnorm(x, sdlog = 0.1) + 0.1*dnorm(x, 2)
r1 <- function(n) sample(c(rnorm(round(n*.6)), rlnorm(round(n*.3), sdlog = 0.1), rnorm(round(n*.1), 2)))

set.seed(123)
x <- r1(100)
dd <- density(x, n = 1000)
ld <- logspline(x)
curve(d1(x), from = min(x), to = max(x), n = 1000, bty = "L", 
      main = "Density estimation methods", y = "f(x)", ylim = c(0, 1.6))
rug(x)
lines(dd, lty = 2)
plot(ld, add=TRUE, lty = 3, n = 1000)
legend("topright", lty = c(1, 2, 3), legend = c("True density", "Kernel density", "Logspline"), bty = "n")


# chisquare
d2 <- function(x) dchisq(x, 3, 1)
r2 <- function(n) rchisq(n, 3, 1)

x <- r2(100)
dd <- density(x, n = 1000)
ld <- logspline(x)
curve(d2(x), from = -1, to = 14, n = 1000, bty = "L", 
      main = "Density estimation methods", y = "f(x)", ylim = c(0, 0.3))
rug(x)
lines(dd, lty = 2)
plot(ld, add=TRUE, lty = 3, n = 1000)
legend("topright", lty = c(1, 2, 3), legend = c("True density", "Kernel density", "Logspline"), bty = "n")

The mixture is well approximated by logspline

It does not seem much better at chisquare