MML-10-05: Bias, Variance, Mean Squared Error (MSE) & Consistency of Estimators – Practice Quiz

30 worked single-select and multiselect questions on Bias, Variance, Mean Squared Error (MSE) & Consistency of Estimators. Intended level: Tier 2–4. Prerequisites: QS 10.4.

The sequence develops conceptual interpretation, explicit calculations, ML diagnostics and, where assigned, derivations with carefully stated assumptions. Feedback explains each answer and misconception by content.

Learning objectives: Calculate bias, variance and mean squared estimation error. Prove and apply the MSE decomposition. Compare biased shrinkage and unbiased alternatives. Distinguish finite-sample unbiasedness from consistency. Use convergence and moment assumptions correctly. Diagnose covariance effects in ensemble estimators. Analyze rates, transformations and irreducible prediction noise.

Study references: Goodfellow, Bengio & Courville, Deep Learning; Duke STA 611, Sampling Distributions of Estimators.