Statistics for Mathematicians A Rigorous First Course
This book is intended as a text for Mathematics students taking their first course in Statistics, and grew out of my second-year course for mathematics undergraduates at EPFL. It is a book on “Statistics for Mathematicians” rather than on “Mathematical Statistics”: the intent is not to focus on the deeper mathematical/theoretical aspects of the subject but rather to provide an introduction to the basic notions tailored to the mindset and tastes of the Mathematics student. Mathematics students are sometimes put off by the informal nature of first courses in Statistics, since many results are usually stated without proof or are accompanied by heuristic sketches of proofs. Another risk may be that of “intellectual entropy”, when too many (and diverse) topics are covered in a single course, risking the impression of Statistics as a collection of recipes lacking natural connection. This book can be used as a basis for an elementary semester-long first course in Statistics that presents the basic ideas of one-parameter inference in a coherent manner, while making essentially no sacrifices on matters of rigour. It is meant to be compact, so as to be realistic to be covered in full during a single semester, and yet hopefully attract mathematics students to pursuing further elective courses in Statistics. In more detail, the three main tasks this text sets out to address are as follows.