Applied statistics (DVML, MATØK)

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Likelihood and maximum likelihood estimation

Literature

[WMMY] 9.14.

Lecture material

This lecture as: slideshow (html), Rmarkdown (Rmd), notes (pdf).

The entire module: notes (pdf).

Exercises

1. Suppose that X is Binomial(n, p).

   1. What is the maximum likelihood estimator (MLE) of p?

   2. Plot the log likelihood function for n = 10 and X = 5.

   3. Plot the log likelihood function for n = 100 and X = 50.

   4. Plot a) and b) in same figure. How and why are they different?

   5. Use the optimise() (read ?optimise) to find the MLE of p in both cases.

2. Simple linear regression (one explanatory variable)

   1. Write the log likelihood for n observations.

   2. For the trees dataset with Volume as response variable and Girth as explanatory variable, use the optim() to find the parameter estimates and compare to those obtained with summary(lm()).

3. Finish old exercises.