Statistical inference

This page is a draft.

Some discussions about a good book:


Review of probability:

  • random variables, outcomes, probability

  • distributions, pdf/cdf

Mathematic statistics itself:

  • idea: learn about data generating process (DGP) from a sample

  • sample/realisation as a random vector

  • statistic as a function of sample

  • parameter inference:

    • point estimation and methods (estimators)

    • estimator quality (bias, consistency, efficiency)

  • confidence intervals (CI)

  • hypothesis testing (HT), types of errors

  • analysis of variance and regression

See an example of stated learning objectives

Key textbook

Casella, Berger. Statistical Inference.

Other choices

Larry Wasserman. All of Statistics: A Concise Course in Statistical Inference

- [text 1](
- [text 2](
- [Amazon](

Efron, Hastie. Computer Age Statistical Inference: Algorithms, Evidence and Data Science.



James Gentle. A theory of statistics.

De Groot and Shervish%20(1).pdf)

Herman J. Bierens. Introduction to the Mathematical and Statistical Foundations of Econometrics

Aris Spanos. Probability Theory and Statistical Inference: Econometric Modeling with Observational Data.

- [link](

Probability and Statistics for Engineers and Scientists (PSES)

Other reading

Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars

- [Amazon](
- very philosophic reading

Peter M. Aronow, Benjamin T. Miller. Foundations of Agnostic Statistics.

- [Google Book (fragments)](
- [book proposal](
- simplictic

In Russian

Cramer, 1946, Russian translation, timeless! also has dataset if wheat yeilds.

Also concise version of lectures here (in Russian)