Can you really solve for an MLE given a fictitious distributi

#1
to estimate MLE, you need more than one observation, right? What if you don't have a density function? (It's a fictitious disitrubtion)
 
Last edited:

BioStatMatt

TS Contributor
#2
In order to form a maximum likelihood estimate (MLE), you must have a likelihood function. If \(y_1, \ldots, y_n \sim f(y_i|\theta)\), where \(f(y_i|\theta)\) is a density function indexed by \(\theta\), then the likelihood function is given by \(L(\theta|y_1,\ldots,y_n) = \prod_{i=1}^n f(y_i|\theta)\). Of course, without an explicit density function, we can't go much farther than this in computing an MLE.

In general, no more than one observation is required in order to compute a MLE. However, the MLE may not be unique. This problem is called unidentifiability. That is, when there are few observations, the MLE may be a poor estimate of \(\theta\).
 

fed1

TS Contributor
#3
Just to be totally confusing I wan to point out that there is
non parametric maximum liklihood (MELE) that leads to k-m and empirical cdf. Not alot to say about one observation though!! :yup:
 
#4
BioStatMatt is correct.
Without disitrubtion function , cann't get maximum likelihood estimate .
But for k-m , using empirical distribution , it would be better with more observations.