Distribution Theory of Least Squares

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Page 3 of 4

Delves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.

Likelihood Ratio Tests: Optimality and Extensions

Covers Likelihood Ratio Tests, their optimality, and extensions in hypothesis testing, including Wilks' Theorem and the relationship with Confidence Intervals.

Estimating Parameters: Confidence Intervals

Explores estimating parameters through confidence intervals in linear regression and statistics.

Inference and Mixed Models

Covers point estimation, confidence intervals, and hypothesis testing for smooth functions using mixed models and spline smoothing.

Error Estimation in LHS

Covers error estimation in Latin Hypercube Sampling, emphasizing the importance of accurate variance estimation.

Statistical Tests: T-Tests and ANOVA

Covers the calculation of paired t-tests, advantages/disadvantages of different t-tests, and the concept of ANOVA.

Linear Regression: Least Squares

Delves into linear regression, emphasizing least squares estimation, residuals, and variance.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Regression Analysis: Multivariate Data Modeling

Introduces regression analysis for multivariate data modeling, covering matrix algebra, interpretation of coefficients, and test intervals.

Confidence Intervals and Hypothesis Testing

Explores confidence intervals, hypothesis testing, and decision-making using test statistics and p-values.