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.