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?

## Best Answer

The

`mgcv`

package can fit generalized additive models from many families of distributions including the Gumbel distribution.The authors provide the following example: