5
votes
Accepted
MLE and non closed-form solutions - how to see or proof it?
Take the standard classical OLS model:
$$ \mathbf{y} = \mathbf{\beta} \mathbf{X} + \epsilon $$
where $\mathbf{\beta}$ is a vector and $\mathbf{X}$ is a matrix. There is a closed form solution for $\...
- 2,667
4
votes
Does the MLE converge in mean-square?
An example of an MLE that converges in probability but not in mean square is the ratio of two binomials. Let $X_n\sim Bin(n,p)$ and $Y_n\sim Bin(n,q)$, then the MLE of $(p,q)$ is $(\bar X_n, \bar Y_n)...
- 43.3k
1
vote
Maximum Likelihood Estimation -- why it is used despite being biased in many cases
Unbiasedness is sometimes a very bad thing. An example is found in this paper that I wrote, which appeared in the American Mathematical Monthly.
Hardy, M. (2003). "An Illuminating Counterexample.&...
- 10.7k
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