Cover illustration for The Shape of Statistical Theory.

The Shape of Statistical Theory

How the pieces of theoretical statistics fit — distributions, estimation, risk, and regularization, from intuition up.

I · The Language of Distributions

1What This Book Is About 2Random Variables and Distributions 3Expectation, Moments, and Their Uses 4Families of Distributions 5Convergence and the Limit Theorems

II · Estimation

6What Makes a Good Estimator 7Sufficiency and Information 8Maximum Likelihood 9The Bayesian View

III · Loss, Risk, and Decisions

10Loss Functions: What You Are Rewarding 11Risk and Decision Theory 12The Bias–Variance Tradeoff

IV · Regularization and Shrinkage

13The Shrinkage Surprise 14Penalties and Priors 15Choosing the Penalty

V · Testing and Inference

16Hypothesis Testing 17P-values, Power, and Errors 18Confidence and Credible Intervals

VI · Asymptotics and the Modern View

19Asymptotic Efficiency 20The Bootstrap 21High-Dimensional Phenomena

Appendices

AA Probability Refresher BGlossary