Parameter Estimation Overview - Pillai

This video is based on Lecture#12 by Prof.Pillai. https://acrobat.adobe.com/id/urn:aaid:sc:VA6C2:bf285a07-bd8f-4d45-9bef-d12c97bd58a8 The provided text discusses the fundamental principles of parameter estimation, focusing on methods for determining an unknown, nonrandom parameter (theta) from noisy observations. A primary strategy explored is the Maximum Likelihood (ML) estimation, which selects the parameter value that maximizes the likelihood function based on observed data. The text provides examples illustrating the application of ML estimation for both linear and highly nonlinear cases, evaluating estimators based on properties like being unbiased (having an expected value equal to the true parameter) and consistent (variance approaching zero as the number of observations increases). Furthermore, it introduces the Cramer-Rao Bound as the theoretical lower limit on the variance of any unbiased estimator, defining efficient estimators as those that meet this bound. Finally, the source briefly contrasts ML estimation with the Maximum A-Posteriori (MAP) estimation, a Bayesian approach used when the parameter itself is a random variable with an a priori probability density function.