Elements of Large-Sample Theory

by Erich L. Lehmann

Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

Genres: Mathematics, Textbooks, Science

644 pages, Hardcover

First published December 4, 1998

Reviews

[David Bickel · Rating 5 out of 5]

simple expositions of difficult concepts

[Anurag · Rating 5 out of 5]

An absolute treat to those who are tired of just intuitive explanations in their statistics classes – but have also struggled with the heavy mathematics that is used in the development of statistical theories. That is not to say that the textbook does not rely on intuitive explanations. Instead, it beautifully connects the mathematical ideas with the elements of serious analysis. The book never assumes a pure mathematical background or even a course in measure theory, but it still steers through complex topics with clarity.

The pure mathematician may be uneasy with many of the theorems being stated without proofs, but the book always either sketches a proof or provides a counter-example to explain why the math proceeds the way it does. This makes the text far better than the recipe-based books that have littered the literature. Instead of using software solutions and graphical explanations, the book attempts to provide the reader an ability to develop the concepts from the ground up. That this can be achieved without a rigorous proof-based approach is in itself an achievement (although the reader is referred to more advanced books - particularly Billingsley and Feller - throughout the book).

[Tim · Rating 3 out of 5]

This is the textbook we used for Large-sample theory course. Lehmann is a very big name in Stats. But this book does not match his name. First, MANY MANY references are used in this book, making reading really annoying. Also, there are small mistakes on many page if you read and think carefully. My instructor caught many places not reasonable.
　　
But I guess it is not easy at all to write a thick book in this area.

[KT · Rating 4 out of 5]

Used as a reference book - did not read front-to-back nor am I a college student giving a review of how well this textbook augments a professor's class. I wouldn't say this book is "very modern" like others. It is, tho, written in a way that it's easy to flip to a section and pick up the concepts you need without needing tons of granular info.