How to Find Maximum Likelihood Estimators for Sample Data?

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SUMMARY

The discussion focuses on finding Maximum Likelihood Estimators (MLE) for sample data using the likelihood function L(x,p) = ∏_{i=1}^n pdf and the log-likelihood function l = ∑_{i=1}^n log(pdf). Participants express confusion about applying these equations when only sample data is available, as opposed to a given probability density function (pdf). The solution involves solving the derivative of the log-likelihood function, ∂l/∂p = 0, to estimate the parameter p.

PREREQUISITES
  • Understanding of Maximum Likelihood Estimation (MLE)
  • Familiarity with probability density functions (pdf)
  • Knowledge of calculus, specifically derivatives
  • Experience with statistical sampling techniques
NEXT STEPS
  • Study examples of MLE with sample data in statistical textbooks
  • Learn about the application of log-likelihood functions in parameter estimation
  • Explore online resources or tutorials on MLE using sample data
  • Consult with a graduate teaching assistant for advanced insights on MLE
USEFUL FOR

Students in statistics or data science, researchers working with sample data, and anyone seeking to understand Maximum Likelihood Estimation techniques.

Scootertaj
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problem.jpg

Homework Equations



[tex]L(x,p) = \prod_{i=1}^npdf[/tex]
[tex]l= \sum_{i=1}^nlog(pdf)[/tex]
Then solve [tex]\frac{dl}{dp}=0[/tex] for p (parameter we are seeking to estimate)

The Attempt at a Solution



I know how to do this when we are given a pdf, but I'm confused how to do this when we have a sample.
 
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Scootertaj said:
problem.jpg



Homework Equations



[tex]L(x,p) = \prod_{i=1}^npdf[/tex]
[tex]l= \sum_{i=1}^nlog(pdf)[/tex]
Then solve [tex]\frac{dl}{dp}=0[/tex] for p (parameter we are seeking to estimate)

The Attempt at a Solution



I know how to do this when we are given a pdf, but I'm confused how to do this when we have a sample.

Are there no similar examples solved in your textbook or course notes? Could you find nothing at all on-line?

RGV
 
Not so far, though I'll be talking to a graduate TA about it.
 

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