Statistical Models: Sampling and Hypothesis Testing

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Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

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.

Eliminating Nuisance Parameters: Statistical Inference

Covers the elimination of nuisance parameters in statistical inference using Lemmas 14 and 15.

Statistical Theory: Inference and Sufficiency

Explores statistical inference, sufficiency, and completeness, emphasizing the importance of sufficient statistics and the role of complete statistics in data reduction.

Testing: t-tests

Covers t-tests, p-values calculation, and comparison of coefficients.

Sampling: Inference and Statistics

Explores sampling in inferential statistics, emphasizing the impact of sample size and randomness on inference accuracy.

Detection & Estimation

Covers the fundamentals of detection and estimation theory, focusing on mean-squared error and hypothesis testing.

Decision Theory: Risk and Hypothesis Testing

Covers decision theory, risk functions, and hypothesis testing in statistical inference.

Special Families of Models

Explores completeness, minimal sufficiency, and special statistical models, focusing on exponential and transformation families.

Sampling Distributions: Estimators and Variance

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