By this, I mean that we can determine the value of the parameter by equating the first derivative of the maximum likelihood function to zero. But it some cases there is a need to determine its variance. how can we calculate it? Does there exist software to perform such an analysis?
Moreover, if a model contains 2 or more then 2 parameters, then how is the covariance between those parameters calculated?
You can use the 2nd. derivative (i.e. the Hessian) to estimate the variance.
See e.g. Chapter 5 in http://www.sherrytowers.com/mle_introduction.pdf
or https://www.stat.berkeley.edu/~nolan/stat135/HO/AsyVar.pdf.
Dear Priyanka Gupta
Please find the attached links, which will help you to short out the problem.
1. http://dawenl.github.io/files/mle_biased.pdf
2. https://socialsciences.mcmaster.ca/jfox/Courses/SPIDA/mle-mini-lecture-notes.pdf
3. https://www.math.arizona.edu/~jwatkins/o-mle.pdf
4. http://www.fao.org/3/X8498E/x8498e0e.htm
with regards
Sumit Maheshwari
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