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Introduction to Data Science (DS 215)
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Module 6
Optimality and Performance of Estimators
1
The Cramer-Rao Lower Bound: Conditions and Derivation
State the conditions for and derive the Cramer-Rao Lower Bound (CRLB).
2
CRLB: Benchmarking Estimator Variance
Explain the significance of the CRLB as a benchmark for an estimator's variance.
3
Proof of the Gauss-Markov Theorem
Prove the Gauss-Markov theorem for the optimality of Ordinary Least Squares (OLS) estimators.
4
Deriving the Best Linear Unbiased Estimator (BLUE)
Derive the Best Linear Unbiased Estimator (BLUE) for a general linear model.
5
MLE vs. OLS for Linear Models with Gaussian Noise
Compare the properties of MLE and OLS estimators for the linear model with Gaussian noise.
Previous module
Maximum Likelihood and Least Squares Estimation
Next module
Principles of Bayesian Inference