Contents
How to calculate the MLE of an unknown parameter?
For large sample sizes, the variance of an MLE of a single unknown parameter is approximately the negative of the reciprocal of the the Fisher information I( ) = E
How is maximum likelihood estimation applied to a vector valued parameter?
Maximum likelihood estimation can be applied to a vector valued parameter. For a simple random sample of nnormal random variables, we can use the properties of the exponential function to simplify the likelihood function.
Is there an asymptotic standard error in ML estimation?
In ML estimation, in many cases what we can compute is the asymptotic standard error, because the finite-sample distribution of the estimator is not known (cannot be derived). Strictly speaking, $hat alpha$ does not have an asymptotic distribution, since it converges to a real number (the true number in almost all cases of ML estimation).
What is meant by the standard error of a maximum?
Because α is unknown, we can plug in ˆα to obtain an estimate the standard error: SE(ˆα) ≈ √ˆα2 / n ≈ √4.69312 / 5 ≈ 2.1 Thanks for contributing an answer to Cross Validated! Please be sure to answer the question.
Which is the maximum likelihood estimator for JX?
The maximum likelihood estimator (MLE), ^(x) = argmax L( jx): (2) Note that if ^(x) is a maximum likelihood estimator for , then g(^ (x)) is a maximum likelihood estimator for g( ). For example, if is a parameter for the variance and ^ is the maximum likelihood estimator, then p ^ is the maximum likelihood estimator for the standard deviation.
Which is an example of an unbiased estimator?
By saying “unbiased”, it means the expectation of the estimator equals to the true value, e.g. if E[x] = hen the mean estimator is unbiased. Now we will show that the equation actually holds for mean estimator. i] is actually E[x]. From the proof above, it is shown that the mean estimator is unbiased.