Statistical Theory

This is the fourth edition of a classic textbook. It will be suitable for a first course in the theory of statistics for students with a solid background in calculus, including multivariate calculus and the elements of matrix algebra. The first third of the book presents basic probability and distribution theory with an eye to their subsequent uses in statistical inference. The second part deals with the basic problems of statistical inference -drawing conclusions from data- with a strong emphasis on likelihood and sufficiency. The awkwardness and pitfalls in classical estimation and hypothesis testing paradigms are pointed out and some Bayesian methods are introduced.