Mathematical Statistics

Ever since my days as a student, economists, doctors, physiologists, biologists, and engineers have come to me with queries of a statistical nature. This book is the product of my long interest in practical solutions to such problems. Study of the literature and my own ideas have repeat- edly led me to improved methods, which will be established here and applied to instructive examples taken from the natural and social sciences. Thus, I hope to help the reader avoid the many fruitless direc- tions in which I worked at first. The examples are not artificially con- structed from theoretical considerations but are instead taken from real situations; consequently, many of the examples require detailed explana- tion. The presentation of the basic mathematical concepts is, I hope, as brief as possible without becoming incomprehensible. Some rather long theoretical arguments have been necessary, but, whenever possible, references for the more difficult proofs have been made to good text- books already in existence. There would be no point in developing again the mathematical theories which have been presented clearly and in detail by Kolmogorov, Caratheodory, and Cramer.