Maximum Likelihood Estimator

[Anonymous No.5314158]

What is a Maximum Likelihood Estimator? We learned this in my Prob. & Stats. class and I have no idea how to apply it.

Is it just a function used to estimate for point estimates of a certain parameter of a certain distribution? Or is it way more complicated than that? I may be confusing it with the Likelihood function.

[Anonymous No.5315320]

At least it looks great.

[Anonymous No.5315338]

It has some interesting properties. Btw, I'm sure it is somehow connected with eigenvalues.

[Anonymous No.5315390]

>>5315338
Yes, it looks like a generalization of eigenvalues. You can prove this through using matrices - usually the effective method.

[EconPoser !nHKvW0t1cI No.5316191]

Might be coming in late here, but whatever.

A Maximum Likelihood Estimator kind of takes the opposite approach of the OLS method (though the results can coincide under special circumstances). Rather than taking a dataset as a representation of the population as given, and trying to find what characteristics this population might have when it comes to specific variables, you start off from a distributional assumption and try to find the parameters that would make finding your dataset the most likely.

Basically, you try to find out what parameter values would make obtaining your specific sample as likely as possible.

The use of a likelihood function is necessary during this procedure. Based on your distribution (Bernoulli, Normal, Gamma, whatever you like), you formulate a function for each of your observations. This likelihood function basically gives you the probability of obtaining a specific set of observations (contingent on values of the dependent variable), and the function is dependent on a parameter vector. By maximising this function with respect to the parameter set, you find out what parameters would maximise the probability of having your specific sample.

Hope that helped a bit.