Order
Programmable maximum likelihood
Various methods available 
- Linear-form methods; no need to code derivatives
- No-derivative methods; no need to code derivatives
- First-derivative methods; must code first derivative
- Second-derivative methods; must code first and second derivatives
- Write code in ado or Mata
Debugging
- Utility to verify that the log likelihood works
- Ability to trace the execution of the log-likelihood evaluator
- Comparison of numerical and analytic derivatives
Techniques
- Modified Newton–Raphson
- Davidon–Fletcher–Powell (DFP)
- Broyden–Fletcher–Goldfarb–Shanno (BFGS)
- Berndt–Hall–Hall–Hausman (BHHH)
Variance matrix estimators
- Observed information matrix (Hessian matrix)
- Outer product of the gradients (OPG)
- Huber/White/robust and cluster–robust
- Bootstrap
- Jackknife
- Survey design, including multistage and stratified designs
See New in Stata 18 to learn about what was added in Stata 18.
