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anyone knows some used case scenarios where Maximum likelihood estimator(MLE) fails to predict the right answer? with an exception of the problems which may require infinite computations, or samples or are NP-hard.

inoor
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    Hi user892713. This seems like a rather under-specified /overly general/vague question. You may wish to make it more focused. In addition you might include what considerations you have already investigated. – WestCoastProjects Dec 07 '15 at 03:18
  • Also, your question requires improvement, but _might_ be a better fit for CrossValidated _if_ you improve it. – Richard Erickson Dec 07 '15 at 03:24

2 Answers2

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MLE is guaranteed to converge to the correct solution when the solution space is convex conic. That is, it converges to a single correct answer when the response space has a curvature that is always positive or negative. That condition may be slightly over-restricted. If the optimal solution is a plateau of some sort, then it should also converge.

Hence, MLE is not guaranteed to converge under other circumstances. For instance, if you take the function of altitude in North American and you are trying to use MLE to find the highest point, then it is highly, highly unlikely that you will converge to Denali. You might get lucky with the right initial conditions.

That is a continuous case. It is also not guaranteed to converge if there are any discontinuities in the response space.

Gordon Linoff
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  • nit: it's just 'Denali' not Mount ;) – WestCoastProjects Dec 07 '15 at 03:22
  • agreed. convergence may depend on the optimization algorithm as well. my question was to bring up cases where the conditional probabilities might fail to model the scenario, regardless of computation required. apologies if question was not specific enough. – inoor Dec 07 '15 at 03:36
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You normally expect MLE to get closer and closer to the right answer as you gather more and more data - consistency. One case where this does not happen is if the number of unknown parameters increases as you gather more data, even if you don't actually care about the values of the unknown parameters. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.201.5098&rep=rep1&type=pdf - The incidental parameter problem since 1948, by Lancaster - is a survey paper on the statistics of this case and starts with a simple example of this (P3).

mcdowella
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