1. Given the observed data {𝑥1, … , 𝑥𝑛}, which is the most likely population parameter 𝜃 that has generated the observations?
2. Requires
   1. The underlying distribution of each random variable is explicitly known and that the sample data match this distribution
   2. the observations are statistically independent (Could transfer auto-correlated observation to independent)
3. Transforming into logarithmic form
   1. Monotonically increasing
   2. Transfer Product to Summation
   3. Easy to find maximum (Derivatives of summations can skip the product rule)
4. Properties
   1. ML estimators are asymptotically unbiased
   2. The ML estimator is asymptotically consistent
   3. ML estimators are asymptotically normally distributed
   4. Comparable test statistics to the t-test, F-test and partial F-test can be calculated
5. Test
   1. The Wald test
      1. Full model with all parameters is estimated
      2. a substitute for the single t-test (deviation over the standard error)
   2. Likelihood Ratio Test (LR)
      1. Chi 2 = -2 * (ln(L[k-h]) - ln(L[k]) )) with h degrees of freedom
      2. Like partial F test