Optimality in Decision Theory: Unbiased Estimation

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Explores the application of linear algebra in data science, covering variance reduction, model distribution theory, and maximum likelihood estimates.

Likelihood Ratio Tests: Optimality and Applications

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

Parameter Estimation: Detection & Estimation

Covers the concepts of parameter estimation, including unbiased estimators and Fisher information.

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Maximum Likelihood Estimation

Delves into maximum likelihood estimators, their properties, and asymptotic behavior, emphasizing consistency and asymptotic normality.

Model Selection Criteria: AIC, BIC, Cp

Explores model selection criteria like AIC, BIC, and Cp in statistics for data science.

Fisher Information, Cramér-Rao Inequality, MLE

Explains Fisher information, Cramér-Rao inequality, and MLE properties, including invariance and asymptotics.

Sampling Distributions: Estimators and Variance

Covers estimation of parameters, MSE, Fisher information, and the Rao-Blackwell Theorem.

Parameter Estimation

Introduces statistical inference concepts, focusing on parameter estimation, unbiased estimators, and mean estimation using independent random variables.

Bias, Variance, Consistency, EMV

Covers bias, variance, mean squared error, consistency, and maximum likelihood estimation in the Poisson model.