The regression estimation problem has a long history. Already in 1632 Galileo Galilei used a procedure which can be interpreted as ?tting a linear relationship to contaminated observed data. Such ?tting of a line through a cloud of points is the classical linear regression problem. A solution of this problem is provided by the famous principle of least squares, which was discovered independently by A. M. Legendre and C. F. Gauss and published in 1805 and 1809, respectively. The principle of least squares can also be applied to construct nonparametric regression estimates, where one does not...

Principal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques it continues to be the subject of much research, ranging from new model- based approaches to algorithmic ideas from neural networks. It is extremely versatile with applications in many disciplines. The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material,...

Bayesian nonparametrics has grown tremendously in the last three decades, especially in the last few years. This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. While the book is of special interest to Bayesians, it will also appeal to statisticians in general because Bayesian nonparametrics offers a whole continuous spectrum of robust alternatives to purely parametric and purely nonparametric methods of classical statistics. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian...

During the last decades, there has been an explosion in computation and information technology. This development comes with an expansion of complex observational studies and clinical trials in a variety of fields such as medicine, biology, epidemiology, sociology, and economics among many others, which involve collection of large amounts of data on subjects or organisms over time. The goal of such studies can be formulated as estimation of a finite dimensional parameter of the population distribution corresponding to the observed time-dependent process. Such estimation problems arise in...

The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in...

This edition contains a large number of additions and corrections scattered throughout the text, including the incorporation of a new chapter on state-space models. The companion diskette for the IBM PC has expanded into the software package ITSM: An Interactive Time Series Modelling Package for the PC, which includes a manual and can be ordered from Springer-Verlag. * We are indebted to many readers who have used the book and programs and made suggestions for improvements. Unfortunately there is not enough space to acknowledge all who have contributed in this way; however, special mention...

The reader will soon find that this is more than a "how-to-do-it" book. It describes a philosophical approach to the use of statistics in the analysis of clinical trials. I have come gradually to the position described here, but I have not come that way alone. This approach is heavily influenced by my reading the papers of R.A. Fisher, F.S. Anscombe, F. Mosteller, and J. Neyman. But the most important influences have been those of my medical colleagues, who had important real-life medical questions that needed to be answered. Statistical methods depend on abstract mathematical theorems and...

This book arrays recent research on the neural and behavioral lateralization of the brain relying heavily on animal modes. The authors employ the comparative method to enhance our understanding of behavior, specifically through hand use and "handedness" by drawing comparisons with studies involving primates. Topics discussed include Patterns of Lateralized Behavior in Prosimians; Behavioral Lateralization in Language-Trained Chimpanzees; Patterns of Handedness: Comparative Study of Nursery School Children and Captive Gorillas; and Rotational Behavior in Children and Adults. It is the first...

This IMA Volume in Mathematics and its Applications SINGULARITIES AND OSCILLATIONS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering. " We would like to thank Joseph Keller, Jeffrey Rauch, and Michael Taylor for their excellent work as organizers of the meeting. We would like to express our further gratitude to Rauch and Taylor, who served as editors of the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office...

This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random e?ects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the ?rst order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its...