Foundations of Estimation Theory for JAM Statistics

Are you preparing for the JAM Mathematical Statistics exam and looking to master the core mathematical concepts of parameter estimation? Understanding how to find, evaluate, and apply estimators is crucial for scoring high on competitive statistics examinations. This text-only course guides you through the entire landscape of estimation theory, transitioning you from basic probability concepts to advanced statistical inference. You will learn to analyze estimator properties, derive confidence intervals, and apply these mathematical frameworks to exam-style problems. What you'll learn: - Understand foundational definitions of parameters, estimators, and statistical inference. - Evaluate estimator properties including unbiasedness, consistency, efficiency, and sufficiency. - Master classical estimation methods such as Maximum Likelihood Estimation and the Method of Moments. - Apply the Cramer-Rao Lower Bound to find Minimum Variance Unbiased Estimators. - Construct confidence intervals for key population parameters under various distribution assumptions. - Explore modern computational estimation concepts, including simulation-based checks for estimator behavior. The course starts with fundamental definitions and core terminology before moving step-by-step through mathematical proofs, solved derivations, and written practice problems tailored for exam preparation. It is designed for student candidates preparing for the JAM Statistics exam or any undergraduate student seeking a solid, beginner-friendly foundation in mathematical statistics. No advanced prior knowledge of inference is required, though basic probability is recommended. Start reading today to master estimation theory and elevate your analytical exam prep.