The Maximum Likelihood Estimator (MLE) is a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function. It is commonly used to find the most likely values for the parameters of a function based on a set of observed data.
The MLE works by finding the values of the parameters that make the observed data the most likely to occur. This is done by calculating the likelihood of the data for different values of the parameters and then choosing the values that give the highest likelihood.
The MLE assumes that the data is independent and identically distributed (IID). This means that each data point is unrelated to the others and is drawn from the same probability distribution. It also assumes that the data is continuous and that the function being estimated is well-behaved.
The MLE has several advantages, including being a widely-used and well-studied method, being relatively easy to implement, and producing unbiased estimates. It also has good asymptotic properties, meaning that as the sample size increases, the estimates will approach the true values of the parameters.
One limitation of the MLE is that it requires the data to be continuous and have a well-defined probability distribution. It also assumes that the data is independent and identically distributed, which may not always be the case in real-world scenarios. Additionally, the MLE can be sensitive to outliers in the data, which can affect the accuracy of the estimated parameters.