Series: Springer Series in Statistics
2009, Approx. 285 p., Hardcover
ISBN: 978-0-387-92869-2
Due: August 2009
This second edition has over 100 pages of new material
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 semiparametric statistical methods provide a way to reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. These methods are applicable to a wide variety of estimation problems in empirical economics and other fields, and they are being used in applied research with increasing frequency.
The literature on nonparametric and semiparametric estimation is large and highly technical. This book presents the main ideas underlying a variety of nonparametric and semiparametric methods. It is accessible to graduate students and applied researchers who are familiar with econometric and statistical theory at the level taught in graduate-level courses in leading universities. The book emphasizes ideas instead of technical details and provides as intuitive an exposition as possible. Empirical examples illustrate the methods that are presented.
This book updates and greatly expands the authorfs previous book on semiparametric methods in econometrics. Nearly half of the material is new.
Joel L. Horowitz is the Charles E. and Emma H. Morrison Professor of Market Economics at Northwestern University. He is the author of over 100 journal articles and book chapters in econometrics and statistics, a winner of the Richard Stone prize in applied econometrics, a fellow of the Econometric Society and American Statistical Association, and a former co-editor of Econometrica.
Introduction.- Single index models.- Nonparametric additive models and semiparametric partially linear models.- Binary response models.- Statistical inverse problems.- Transformation models.- Appendix: Nonparametric density estimation and nonparametric regression.
Series: The IMA Volumes in Mathematics and its Applications , Vol. 150
2009, Approx. 350 p., Hardcover
ISBN: 978-1-4419-0669-4
Due: September 2009
Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on
Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15--21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give and overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital
life processes.
Foreword.-Preface.-Nick Cozzarelli: A personal remembrance.-Mathematical methods in DNA topology:Applications to chromosome organization and site-specific recombination.-Conformational statistics of DNA and diffusion equations on the Euclidean group.-Perspectives on DNA looping.-Differences between positively and negatively supercoiled DNA that topoisomerases may distinguish.-Calibration of tethered particle motion experiments.-Difference topology: Analysis of high-order DNA-protein assemblies.-Useful intrusions of DNA topology into experiments on protein-DNA geometry.-Topological analysis of DNA-protein complexes.-Closing the loop on protein-DNA interactions:Interplay between shape and flexibility in nucleoprotein assemblies having implications for biological regulation.-Four-way helical junctions in DNA molecules.-Micromechanics of single supercoiled DNA molecules.-Flexibility of nucleosomes on topologically constrained DNA.-The mathematics of DNA structure, mechanics, and dynamics.-Paradox regained: a topological coupling of nucleosomal DNA wrapping and chromatin fibre coiling.-Statistical-mechanical analysis of enzymatic topological transformations in DNA molecules.-List of workshop participants
Series: Birkhauser Advanced Texts / Basler Lehrbucher
2009, Approx. 560 p. 21 illus., Hardcover
ISBN: 978-0-8176-4306-5
A Birkhauser book
Due: October 2009
Fascinating historical commentary interwoven into the exposition
Hundreds of problems from routine to challenging
Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects
Two significant appendices on functional analysis and Fourier analysis
In-depth development of measure theory and Lebesgue integration
Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results
Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals
Evolution of the Riesz representation theorem to Radon measures and distribution theory
Deep results in modern differentiation theory
Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn?Saks
Thorough treatment of rearrangements and maximal functions
The relation between surface measure and Hausforff measure
Complete presentation of Besicovich coverings and differentiation of measures
A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental modern results such as the Dieudonne?Grothendieck theorem and other intricate developments dealing with weak convergence of measures.
Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.
Preface.-Classical real variables.-Lebesgue measure and general measure theory.-The Lebesgue integral.-The relationship between differentiation and integration on R.-Spaces of measures and the Radon?Nikodym theorem.-Weak convergence of measures.-Riesz representation theorem.-Lebesgue differentiation theorem on Rd.-Self-similar sets and fractals.-Appendix I: Functional analysis.-Appendix II: Fourier Analysis.-References.-Index
2010, Approx. 600 p. 52 illus., Hardcover
ISBN: 978-3-642-01776-6
Due: November 2009
Symplectic Geometry Algorithms for Hamiltonian Systems will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.
Chapter 1: Preliminaries of Differential Manifolds.- Chapter 2: Symplectic Algebra and Geometry Preliminaries.- Chapter 3: Hamiltonian Mechanics and Symplectic Geometry.- Chapter 4: Symplectic Difference Schemes for Hamiltonian Systems.- Chapter 5: General Theory for Construction of Symplectic Schemes of HamiltonianSystems.- Chapter 6: Calculus of Generating Function and Formal Energy Hamiltonian Algorithm.- Chapter 7: Symplectic Runge-Kutta Methods.- Chapter 8: Composition Scheme.- Chapter 9: Formal Power Series.- Chapter 10: Volume-Preserving Schemes for Source-Free Systems.- Chapter 11: Contact Algorithms for Contact Dynamic Systems.- Chapter 12: Poisson Bracket and Lie-Poisson Bracket.-
Series: Sources and Studies in the History of Mathematics and Physical Sciences
2010, Approx. 400 p. 16 illus., Hardcover
ISBN: 978-0-387-87856-0
Due: April 2010
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications.
Preface.- Introduction.- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods.- The hypothesis of elementary errors.- Chebyshev's and markov's contributions.- The way towards modern probability.- General limit problems.- Conclusion: the central limit theorem as a link between classical and modern probability.- Index.- Bibliography