GAM with non-normal noise I am starting to work with GAM models, and I am trying to figure out the consequences of having non-normal noise. Consider the following example (just note that Gumbel(-0.57, 1) is a centered continued distribution with a finite variance, but skewed):
n=1000;
X1=rexp(n); X2=runif(n, 0, 5); Y=-2 + sin(X1) + X2^3 + rgumbel(n, -0.57, 1);

fit=gam(Y~s(X1)+s(X2))

So, can I somehow take into account that the noise is non-normal? Do I have to?
Some motivation: I am actually trying to estimate the distribution of the noise variables here (as they have a specific interpretation in my problem). So I would like to see something like fit$residuals having approximately Gumbel distribution. Is it true though that as $n\to\infty$ we would not reject ks.test(fit$residuals, Gumbel)? Or in other words, are the estimations of $\hat{f}_1,\hat{f}_2$ consistent even if we don't have normal noise?

You could fit the model, say m1, using the gamlss R package:
m1 <- gamlss(Y ~ pb(X1) + pb(X2), family = GU)

However the parameterisation of gumbel and GU may be different.
You could randomly generate observations using gamlss by
mu <- 2 + sin(X1) + X2^3

sigma <- rep(1,1000)

Y <- rGU(1000,mu,sigma)

or
Y <- 2 + sin(X1) + X2^3 + rGU(1000,0,1)

