Statistical Theory: Decision Theory Framework

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (31)

Page 2 of 4

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Optimality in Statistical Inference

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

Hypothesis Testing: A Different Perspective

Delves into a different perspective on hypothesis testing, emphasizing the p-value and significance levels.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Inference and Mixed Models

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

Testing: t-tests

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

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

Detection & Estimation

Covers binary classification, hypothesis testing, likelihood ratio tests, and decision rules.