Book Proposal: Theory of Agnostic Statistics

Reflecting a sea change in how empirical research has been conducted over the past decade, Theory of Agnostic Statistics is a foundational text that develops a formalization of statistical theory for the social and health sciences without invoking strong modeling assumptions. The book represents the first unified, book-length treatment of probability theory, statistical inference and nonparametric identification for applied topics (including missing data and causal inference). We provide a formal justification and a cogent argument for the use of agnostic statistics, a perspective on empirical research that implies minimal assumptions and emphasizes credible inference. We believe that our book is uniquely suited to teach readers the foundational logic of statistics in a manner that prepares them for critical engagement with advanced statistical inference and research methods. Although there exist many textbooks that address nonparametric statistics or causal inference, we believe there is no other book accessible to first-year graduate students that builds from first principles to allow students to understand cutting edge statistical methods. Our book begins with a comprehensive treatment of probability theory and asymptotic statistics in the frequentist paradigm. We then develop the core idea of plug-in estimation, a means of estimating features of probability distributions with little to no additional statistical assumptions