Add convenience function for calculating loss (log-likelihood) over data, also information criterion adjusted

The loss should be using the triangular structure, and thus additive nature of the log-likelihood.
For each sub log-likelihood, we may add the information criterion component.
I.e., we seek to evaluate
$$l(u;\hat{\Lambda})=\sum_j l(u_j;\hat{C}_j)$$

and to evaluate
$$E[l(u_{test};\hat{\Lambda})]$$
as
$$E[l(u_{test};\hat{\Lambda})]\approx \sum_j l(u_{j,~ train};\hat{C}_j) + IC(\hat{C}_j)$$
where we may try for $IC(\hat{C}_j)$
the
- AIC: $IC(\hat{C}_j)=ne(j)+1$, easy, standard, and may be computed locally for $\hat{C}_j$ or globally for $\hat{\Lambda}$. Negative: Asymptotics and assumes population precision is in the family of precisions being estimated over.
- AICc: $IC(\hat{C}_j)=k + \frac{k^2+k}{n-k-1}$ for $k=ne(j)+1$, easy and relatively standard. May only be computed locally on $\hat{C}_j$. It is an adjustment for small sample sizes but requires $k < n$ still. It also has the same assumptions on the population precision as the AIC.
- TIC: $IC(\hat{C}_j)=tr[\nabla^2 l(u_j;\hat{C}_j) (\nabla l(u_j;\hat{C}_j)^2)])$ can be computed locally or globally. Locally makes sense, as we have access to derivatives from the optimization. Avoids the assumptions on population precision.

All of the above employs asymptotic results. Is it possible to use e.g. the bootstrap (or the bootstrap in the frequentist domain) to alleviate these assumptions for when $n$ is small?