Statistical inference

This page is a draft.

Some discussions about a good book:

• Math Overflow: Statistics for Mathematicians

• Stack Exchange: What to learn after Casella/Berger

Topics

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.

• link

Other choices

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

- [text 1](https://www.ic.unicamp.br/~wainer/cursos/1s2013/ml/livro.pdf)
- [text 2](http://static.stevereads.com/papers_to_read/all_of_statistics.pdf)
- [Amazon](https://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/0387402721)

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

- https://web.stanford.edu/~hastie/CASI_files/PDF/casi.pdf

Supplements

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](https://wilfridomtz.files.wordpress.com/2014/08/cambridge-university-press-probability-theory-and-statistical-inference-842pg.pdf)

Probability and Statistics for Engineers and Scientists (PSES)

Other reading

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

- [Amazon](https://www.amazon.com/Statistical-Inference-Severe-Testing-Statistics/dp/1107664640)
- very philosophic reading

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

- [Google Book (fragments)](https://books.google.ru/books?id=u1N-DwAAQBAJ&printsec=frontcover&hl=ru&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)
- [book proposal](http://aronow.research.yale.edu/aronowmillerproposal.pdf)
- simplictic

Papers

Statistical Inference: The Big Picture. Robert E. Kass (2006)

A short history of probability theory and its applications. International Journal of Mathematical Education. January 2015. Kanadpriya Basu.

Video

Placeholder:

• Andrew Gelman - Theoretical Statistics is the Theory of Applied Statistics: How to Think About What We Do

• Andrew Gelman - Solve All Your Statistics Problems Using P-Values

• Andrew Gelman - Barcelona Data Science Meeting

• Andrew Gelman - Crimes against data, Professor Andrew Gelman

In Russian

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

Also concise version of lectures here (in Russian)