Fitting Linear Relationships

This book is intended for students of mathematical statistics who are interested in the early history of their subject. It gives detailed algebraic descriptions of the fitting of linear relationships by the method of least squares (L ) and the related least absolute 2 deviations (L ) and minimax absolute deviations (Loo) procedures. These traditional line J fitting procedures are, of course, also addressed in conventional statistical textbooks, but the discussion of their historical background is usually extremely slight, if not entirely absent. The present book complements the analysis of these procedures given in S.M. Stigler'S excellent work The History of Statistics: The Quantification of Uncertainty before 1900. However, the present book gives a more detailed account of the algebraic structure underlying these traditional fitting procedures. It is anticipated that readers of the present book will obtain a clear understanding of the historical background to these and other commonly used statistical procedures. Further, a careful consideration of the wide variety of distinct approaches to a particular topic, such as the method of least squares, will give the reader valuable insights into the essential nature of the selected topic.

Gives a clear understanding of the historical development of commonly used statistical estimation procedures, an approach which is not found in other books Considers a wide variety of distinct approaches which lead to the same statistical techniques; this gives readers valuable insights into the essential nature of these procedures Of interest to both statisticians concerned with the fitting of linear models, as well as to engineers and scientists working with the empirical determination of linear relationships Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction.- 2 The Methods of Boscovich and Mayer.- 3 Laplace's Work on the Methods of Boscovich and Mayer.- 4 Laplace's Minimax Procedure.- 5 The Method of Least Squares.- 6 Statistical Foundations of the Method of Least Squares.- 7 Adrain's Work on the Normal Law.- 8 Gauss's Most Probable Values.- 9 Laplace's Most Advantageous Method.- 10 Gauss's Most Plausible Values.- 11 Gauss's Method of Adjustment By Correlates.- 12 Mechanical Analogies for the Method of Least Squares.- 13 Orthogonalisation Procedures.- 14 Thiele's Derivation of the Method of Least Squares.- 15 Later Work on the Method of Situation.- 16 Concluding Remarks.- Name Index.