We consider a number of data settings where the use of standard maximum likelihood or other estimation method is complicated for a number of reasons: data structures are complex, there are very large data streams, in reverse there are very small trials (like in orphan diseases), or there are non-standard design features (sequential trials, missing data, clustered data with variable size, etc.).
The use of alternatives to maximum likelihood are explored, with particular emphasis on pseudo-likelihood, split-sample methods, and even closed-form estimators in settings where one would not expect them.
Specific attention is devoted to the computational feasibility of the proposed methods. We pay particular attention to the existence of closed forms in our modified procedures.
All settings are illustrated using real-life examples.
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