Reading Companion for Asymptotic Statistics

This is an unofficial reading companion to A. W. van der Vaart’s Asymptotic Statistics. It is not affiliated with or endorsed by van der Vaart or Cambridge University Press & Assessment.

These reading notes were drafted and organized by an AI assistant (ChatGPT), reviewed and edited by me (Molly Offer-Westort). The notes come out of weekly discussions from a reading group of the book, meeting in the summer of 2026.

The companion is designed to be used alongside the original text, not in place of it. Readers will need a copy of the book for the assigned readings, complete context, and end-of-chapter exercises. The publisher’s edition is available through Cambridge Core.

Path to Chapter 25

In our reading group, our goal was to build up to chapter 25 on semiparametric statistics. The preface of van der Vaart helpfully includes a dependence chart, mapping out some alternative paths to get there; we combined two of these paths, over seven weekly sessions. These reading notes cover chapters 2, 6, 7, 8, 18, 19, and 25.

Paths to chapter 25 include:

\[ 2\longrightarrow6\longrightarrow7\longrightarrow8\longrightarrow25, \qquad 2\longrightarrow18\longrightarrow19\longrightarrow25. \]

Seven-week reading plan

Objective of these notes

The book is dense and does not do a lot of hand-holding, and I found myself wishing for a New Bloomsday Book-style guide that walks the reader through what is going on, explains what previous exposure is assumed, and makes links across chapters more explicit.

These notes are an effort to illustrate some of that structure across chapters in conceptual content, proof techniques, and running examples.
As well, I asked the AI to make connections to other coverage of similar material that our group was familiar with:

  • this incorporates both some background on probability/statistics, including Bailie’s 2021 notes on asymptotic statistics, which touch on material covered in chapters 5, 6, 7, 8, 13, and 14 of van der Vaart; and Sen’s 2022 empirical process lecture notes, which connect most closely to chapters 18 and 19;

  • as well as material on modern double-debiased machine learning methods, including Chernozhukov et al.’s 2016 coverage of this material; Fisher and Kennedy’s 2018 paper building intuition for influence functions visually; and Kennedy’s 2022 review of targeted double machine learning.

I am sure that there are many other connections that could be made—please feel to reach out at mollyow@uchicago.edu if you have suggestions or edits. Full references are included at the end of the notes.