Mathematical Statistics Lecture Info

Evaluating estimators based on unbiasedness, consistency, and efficiency (minimum variance). Interval Estimation (Confidence Intervals)

This brings us to point estimation, the process of choosing a single best guess for the value of a parameter. We evaluate the quality of an estimator through several mathematical criteria. An estimator is considered unbiased if its expected value equals the true parameter value. We also look for consistency, meaning the estimator converges to the true value as the sample size increases toward infinity. Furthermore, efficiency measures the variance of an estimator; among all unbiased estimators, we seek the one with the smallest variance, often referred to as the Minimum Variance Unbiased Estimator. mathematical statistics lecture

Not all estimators are created equal. Mathematical statistics provides criteria to judge them. An estimator is considered unbiased if its expected

Data is considered a random outcome. We model this using random variables (X). The behavior of these variables is described by probability distributions, such as: Normal Distribution ( Not all estimators are created equal