Numerical Analysis for Statisticians - Lange, Kenneth (Springer New York, 1999)
This book, like many books, was born in frustration. When in the fall of 1994 I set out to teach a second course in computational statistics to doctoral students at the University of Michigan, none of the existing texts seemed exactly right. On the one hand, the many decent, even inspiring, books on elementary computational statistics stress the nuts and bolts of using packaged programs and emphasize model interpretation more than numerical analysis. On the other hand, the many theoretical texts in numerical analysis almost entirely neglect the issues of most importance to statisticians. The closest book to my ideal was the classical text of Kennedy and Gentle [2]. More than a decade and a half after its publication, this book still has many valuable lessons to teach statisticians. However, upon reflecting on the rapid evolution of computational statistics, I decided that the time was ripe for an update. The book you see before you represents a biased selection of those topics in theoretical numerical analysis most relevant to statistics. By intent this book is not a compendium of tried and trusted algorithms, is not a consumer's guide to existing statistical software, and is not an exposition of computer graphics or exploratory data analysis. My focus on principles of numerical analysis is intended to equip students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computional complexity, and mathematical modeling share the limelight and take precedence over philosophical questions of statistical inference