Statistics for Mathematicians: A Rigorous First Course

This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.

Table of Contents

Chapter 1 Regular Probability Models
Chapter 2 Sampling from Probability Distributions
Chapter 3 Point Estimation of Model Parameters
Chapter 4 Tests of Hypotheses for Model Parameters
Chapter 5 Confidence Intervals for Model Parameters