A Course in Large-sample and High-dimensional Theory (en Inglés) - Zhiqiang Tan

This book provides a systematic treatment of two central regimes in statistical theory: classical large-sample theory for M- and Z-estimation with a fixed number of parameters, and high-dimensional theory where the number of parameters can be comparable to or larger than the sample size. While the former was developed earlier and remains fundamental, high-dimensional statistical theory has become an indispensable part of modern statistics.

Classical large-sample theory and high-dimensional theory are typically compartmentalized into separate books and courses, which can make it difficult for readers to see how they relate. To foster learning, this book brings them together in a compact and integrated manner, highlighting both their differences and their shared underlying structures.

Assuming a basic knowledge of mathematics and statistics, the book is intended primarily as a graduate textbook for students and researchers in Statistics, Data Science, and related fields. It serves as a useful resource for those wishing to study classical asymptotics and modern high-dimensional theory as cohesive parts of a broader statistical framework.

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