A structured collection of expository notes on topics related to Statistics and Optimization. Each section contains short introductions and, where available, linked PDF notes with derivations, proofs, examples, and references.
Subjects
Notes on the mathematical foundations of probability, including random variables, distribution functions, independence, expectation, conditional expectation, laws of large numbers, and modes of convergence.
Notes on point estimation, sufficiency, unbiasedness, consistency, likelihood theory, hypothesis testing, confidence intervals, and asymptotic inference.
Notes on linear optimization, feasible regions, standard forms, primal and dual formulations, complementary slackness, Farkas' lemma, and simplex geometry.
Notes on convex sets, convex functions, unconstrained and constrained optimization, Lagrangian methods, KKT conditions, and nonlinear programming.
Notes on modelling rare and extreme events, including block maxima, threshold exceedances, generalized extreme value distributions, generalized Pareto models, tail index estimation, and extreme quantile inference.