Confidence Intervals and MLE Limit Theorems

This lecture covers the construction of approximate confidence intervals using the central limit theorem for large sample sizes. It explains how to find confidence intervals for unknown parameters based on normal distributions and the method of maximum likelihood estimation. The regularity conditions required for the validity of these estimators are discussed, along with examples illustrating cases where these conditions are not met. The lecture also compares the behavior of estimators in regular and non-regular cases, highlighting the impact on convergence and the shape of the distribution. Practical implications of these concepts are emphasized.