Applying the maximum likelihood approach with Python
Maximum Likelihood Estimation (MLE) is the most widely used estimation method. It estimates the probability parameters by maximizing a likelihood function. The obtained extremum estimator is called the maximum likelihood estimator. The MLE approach is both intuitive and flexible. It has the following advantages:
- MLE is consistent. This is guaranteed. In many practices, a good MLE means the job that is left is simply to collect more data.
- MLE is functionally invariant. The likelihood function can take various transformations before maximizing the functional form. We will see examples in the next section.
- MLE is efficient. Efficiency means when the sample size tends to infinity, no other consistent estimator has a lower asymptotic MSE than MLE.
With that power in MLE, I bet you just can't wait to try it. Before maximizing the likelihood, we need to define the likelihood function first.
