This book is directed toward students for whom mathematical statistics is or will become an important part of their lives. Obviously, such students should be able to work through the details of 'hard' proofs and derivations. In addition, students at this level should acquire, or begin acquiring, a deep appreciation for the field, including its historical development and its relation to other areas of mathematics and science generally.
This open book is licensed under a Creative Commons License (CC BY). You can download Theory of Statistics ebook for free in PDF format (6.7 MB).
Table of Contents
Distribution Theory and Statistical Models
Basic Statistical Theory
Unbiased Point Estimation
Statistical Inference Based on Likelihood
Statistical Hypotheses and Confidence Sets
Nonparametric and Robust Inference
Important Probability Distributions
Useful Inequalities in Probability
Notation and Definitions
Theory of Statistics
Science and Mathematics
George Mason University
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III pr...
The purpose of the 3rd edition of this book is to give a sound and self-contained (in the sense that the necessary probability theory is included) introduction to classical or mainstream statistical theory. It is not a statistical-methods-cookbook, nor a compendium of statistical theories, nor is it a mathematics book. The book is intended to be a ...
A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects incl...
This book investigates European citizenship after Brexit, in light of the functionalist theory of citizenship. No matter its shape, Brexit will impact significantly on what has been labelled as one of the major achievements of EU integration: Citizenship of the Union. For the first time an automatic and collective lapse of status is observed. It is...
This timely and applied textbook brings together leading scientists to illustrate how key theories and concepts in social psychology help to predict and explain behavior, and can be successfully applied to benefit social and practical problems. It focuses on robust theories and models known for their successful applications and covers a diverse ran...
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability...