Sufficient Statistics: Understanding Data Compression

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Statistical Inference: Model Selection and Nuisance Parameters

Covers model selection, nuisance parameters, and higher-order inference methods in statistical inference.

Exponential Family Distributions

Covers exponential family distributions, natural parameters, sufficient statistics, and logistic regression.

Maximum Likelihood Estimation: Theory and Examples

Covers maximum likelihood estimation, including the Rao-Blackwell Theorem proof and practical examples of deriving estimators.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.

Statistical Inference: Exponential Families and Likelihoods

Explores exponential families, likelihood functions, and model regularity in statistical inference.

Likelihood Ratio Tests: Optimality and Applications

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

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Sampling Distributions: Estimators and Variance

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

Hypothesis Testing and Confidence Intervals: Key Concepts

Provides an overview of hypothesis testing and confidence intervals in statistics, including practical examples and key concepts.