A major portion of the study of the qualitative nature of solutions of differential equations may be traced to the famous 1836 paper of Sturm 1), (here, as elsewhere throughout this manuscript, numbers in square brackets refer to the bibliography at the end of this volume), dealing with oscilla tion and comparison theorems for linear homogeneous second order ordinary differential equations. The associated work of Liouville introduced a type of boundary problem known as a "Sturm-Liouville problem," involving, in particular, an introduction to the study of the asymptotic behavior of solu tions...
A major portion of the study of the qualitative nature of solutions of differential equations may be traced to the famous 1836 paper of Sturm 1), (he...
This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How- ever, when I accepted Professor A. V. Balakrishnan's invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as...
This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests...
Quasi-Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute.
This book presents essential tools for using quasi-Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods uniform and non-uniform random number generation, variance...
Quasi-Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implem...
Sustainability of pension systems, intergeneration fiscal equity under population aging, and accounting for health care benefits for future retirees are examples of problems that cannot be solved without understanding the nature of population forecasts and their uncertainty. Similarly, the accuracy of population estimates directly affects both the distributions of formula-based government allocations to sub-national units and the apportionment of political representation. The book develops the statistical foundation for addressing such issues. Areas covered include classical mathematical...
Sustainability of pension systems, intergeneration fiscal equity under population aging, and accounting for health care benefits for future retiree...
This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics. In addition, the examples-including extended cases studies-are drawn widely from the literature. This book should be of substantial interest both to statisticians and to anyone else working in the area of 'network science'. The coverage of topics in this book is broad, but unfolds in a systematic manner, moving...
This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material ...
The idea for this book came from the time the authors spent at the Statistics and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina starting in fall 2003. The rst author was there for a total of two years, the rst year as a Duke/SAMSI Research Fellow. The second author was there for a year as a Post-Doctoral Scholar. The third author has the great fortune to be in RTP p- manently. SAMSI was and remains an incredibly rich intellectual environment with a general atmosphere of free-wheeling inquiry that cuts across established elds. SAMSI encourages...
The idea for this book came from the time the authors spent at the Statistics and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle...
This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in s- tistics, operationsresearch, andappliedmathematics, aswellasresearchers and practitioners in the ?eld. The present volume was supposed to have a short chapter on nonparametric regression but was intended to deal mainly with inverse problems. However, the chapter on nonparametric regression kept growing to the point where it is now the only topic covered. Perhaps there will be a Volume III. It might even deal with inverse problems. But for now we...
This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in s- ...
Comparing Distributions refers to the statistical data analysis that encompasses the traditional goodness-of-fit testing. Whereas the latter includes only formal statistical hypothesis tests for the one-sample and the K-sample problems, this book presents a more general and informative treatment by also considering graphical and estimation methods. A procedure is said to be informative when it provides information on the reason for rejecting the null hypothesis. Despite the historically seemingly different development of methods, this book emphasises the...
Comparing Distributions refers to the statistical data analysis that encompasses the traditional goodness-of-fit testing. Whereas the latt...
In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a...
In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general tec...
Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distributions of unobserved random variables. Often, it is assumed that functions of interest are linear or that unobserved random variables are normally distributed. Such assumptions simplify estimation and statistical inference but are rarely justified by economic theory or other a priori considerations. Inference based on convenient but incorrect assumptions about functional forms and distributions can be highly misleading. Nonparametric and...
Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distr...
