Eiderman, Vladimir; Samokhin, Mikhail (Eds.)

Selected Topics in Complex Analysis
The Semen Yakovlevich Khavinson Memorial Volume

Series: Operator Theory: Advances and Applications, Vol. 158
2005, VIII, 224 p., Hardcover
ISBN: 3-7643-7251-6

About this book

This volume is dedicated to the memory of the outstanding mathematician S.Ya. Khavinson. It begins with an expository paper by V.P. Havin presenting a comprehensive survey of Khavinson's works as well as certain biographical material. The complete bibliography following this paper has not previously been published anywhere. It consists of 163 items; a considerable part of these cannot be found in easily accessible sources. The book also contains a series of photographs and twelve original peer-reviewed research and expository papers by leading mathematicians worldwide, including the joint paper by S.Ya. Khavinson and T.S. Kuzina (the last publication of S.Ya. Khavinson).

Table of contents

Semyon Yakovlevich Khavinson (1927-2003).- Bibliography of S.Ya. Khavinson.- Contributions by D. Aharonov, C. Beneteau, D. Khavinson and H.S. Shapiro / L. Aizenberg / J.M. Anderson / J.T. Anderson and J. Werner / J.J. Carmona and K.Yu. Fedorovskiy / V.Ya. Eiderman / A.M. Jerbashian / S.Ya. Khavinson and T.S. Kuzina / M. Melnikov and X. Tolsa / X. Pang, S. Nevo and L. Zalcman / W.T. Ross / V.S. Videnskii.

Amrein, Werner; Hinz, Andreas; Pearson, David (Eds.)

Sturm-Liouville Theory, Past and Present

2005, Approx. 360 p., Hardcover
ISBN: 3-7643-7066-1

About this book

This collection of articles on Sturm-Liouville theory is based on lectures presented at the colloquium and workshop held in Geneva on the occasion of Sturm's 200th anniversary. A historical survey of the field is combined with in-depth coverage of later developments and contemporary research in this major area of modern mathematics and its applications. The authors are among the world's leading experts in this field.

Table of contents

Preface.- Scientific Lectures given at the Sturm Colloquium.- Introduction.- Contributions by D. Hinton, B. Simon, W.N. Everitt, J. Weidmann, Y. Last, D. Gilbert, C. Bennewitz and W.N. Everitt, V.A. Galaktionov and P.J. Harwin, C.-N. Chen, R. de. Ri-o, M. Malamud.- Index.

Roger Koenker
University of Illinois, Urbana-Champaign

Quantile Regression

Series: Econometric Society Monographs

Paperback (ISBN-10: 0521608279)
Hardback (ISBN-10: 0521845734)

available from July 2005

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.


? First comprehensive study of quantile regression methods

? Tutorial on associated statistical software in R

? Illustrative applications from a broad variety of disciplines

Contents

1. Introduction; 1.1. Means and ends; 1.2. The first regression: an historical prelude; 1.3. Quantiles, ranks, and optimization; 1.4. Preview of quantile regression; 1.5. Three examples; 1.6. Conclusion; 2. Fundamentals of quantile regression; 2.1. Quantile treatment effects; 2.2. How does quantile regression work?; 2.3. Robustness; 2.4. Interpreting quantile regression models; 2.5. Caution: quantile crossing; 2.6. A random coefficient interpretation; 2.7. Inequality measures and their decomposition; 2.8. Expectiles and other variations; 2.9. Interpreting misspecified quantile regressions; 2.10. Problems; 3. Inference for quantile regression; 3.1. The finite sample distribution of regression quantiles; 3.2. A heuristic introduction to quantile regression asymptotics; 3.3. Wald tests; 3.4. Estimation of asymptotic covariance matrices; 3.5. Rank based Inference for quantile regression; 3.6. Quantile likelihood ratio tests; 3.7. Inference on the quantile regression process; 3.8. Tests of the location/acale hypothesis; 3.9. Resampling methods and the bootstrap; 3.10. Monte-Carlo comparison of methods; 3.11. Problems; 4. Asymptotic theory of quantile regression; 4.1. Consistency; 4.2. Rates of convergence; 4.3. Bahadur representation; 4.4. Nonlinear quantile regression; 4.5. The quantile regression rankscore process; 4.6. Quantile regression asymptotics under dependent conditions; 4.7. Extremal quantile regression; 4.8. The method of quantiles; 4.9. Model selection, penalties, and large-p asymptotics; 4.10. Asymptotics for inference; 4.11. Resampling schemes and the bootstrap; 4.12. Asymptotics for the quantile regression process; 4.13. Problems; 5. L-statistics and weighted quantile regression; 5.1. L-Statistics for the linear model; 5.2. Kernel smoothing for quantile regression; 5.3. Weighted quantile regression; 5.4. Quantile regression for location-scale models; 5.5. Weighted sums of p-functions; 5.6. Problems; 6. Computational aspects of quantile regression; 6.1. Introduction to linear programming; 6.2. Simplex methods for quantile regression; 6.3. Parametric programming for quantile regression; 6.4. Interior point methods for canonical LPs; 6.5. Preprocessing for quantile regression; 6.6. Nonlinear quantile regression; 6.7. Inequality constraints; 6.8. Weighted sums of p-functions; 6.9. Sparsity; 6.10. Conclusion; 6.11. Problems; 7. Nonparametric quantile regression; 7.1. Locally polynomial quantile regression; 7.2. Penalty methods for univariate smoothing; 7.3. Penalty methods for bivariate Smoothing; 7.4. Additive models and the Role of sparsity; 8. Twilight Zone of quantile regression; 8.1. Quantile regression for survival data; 8.2. Discrete Response models; 8.3. Quantile autoregression; 8.4. Copula functions and nonlinear quantile regression; 8.5. High breakdown alternatives to quantile regression; 8.6. Multivariate quantiles; 8.7. Penalty methods for longitudinal data; 8.8. Causal effects and structural models; 8.9. Choquet utility, risk and pessimistic portfolios; 9. Conclusion; A. Quantile regression in R: a vignette; A.1. Introduction; A.2. What is a vignette?; A.3. Getting started; A.4. Object orientation; A.5. Formal Inference; A.6. More on testing; A.7. Inference on the quantile regression process; A.8. Nonlinear quantile regression; A.9. Nonparametric quantile regression; A.10. Conclusion; B. Asymptotic critical values.

Patsy Haccou / Rijksuniversiteit Leiden, The Netherlands
Peter Jagers / Chalmers University of Technology, Gothenberg
Vladimir A. Vatutin / Steklov Institute of Mathematics, Moscow

Branching Processes
Variation, Growth, and Extinction of Populations

Series: Cambridge Studies in Adaptive Dynamics (No. 5)

Hardback (ISBN-10: 0521832209 )

N available from May 2005

Biology takes a special place among the other natural sciences because biological units, be they pieces of DNA, cells, or organisms, reproduce more or less faithfully. As for any other biological processes, reproduction has a large random component. The theory of branching processes was developed especially as a mathematical counterpart to this most fundamental of biological processes. This active and rich research area allows us to make predictions about both extinction risks and the development of population composition, and also uncovers aspects of a population's history from its current genetic composition. Branching processes play an increasingly important role in models of genetics, molecular biology, microbiology, ecology, and evolutionary theory. This book presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians.

? Important for all fields in biology: written with a broad scope

? Important for mathematicians, in particular probabilists, statisticians and applied mathematicians

? Of interest for PhD students as well as established scientists

? Contains contributions from many eminent and well-known scientists

Contents

Preface; Notations; 1. Generalities; 2. Discrete-time branching processes; 3. Branching in continuous time; 4. Large populations; 5. Extinction; 6. Development of populations; 7. Specific models; Appendix; References.

Contributors

Patsy Haccou, Peter Jagers, Vladimir A. Vatutin, Marina Alexandersson, Gerold Alsmeyer, A. D. Barbour, Michel Durinx, Mats Gyllenburg, Goran Hognas, Vincent A. A. Jansen, Fima Klebaner, Marek Kimmel, Thomas G. Kurtz, Johan A. J. Metz, Peter Olofsson, Serik Sagitov, Nico Stollenwerk, Simon Tavare

Edited by J. Rawnsley / University of Warwick
S. Gutt / Universite Libre de Bruxelles
D. Sternheimer / Universite de Bourgogne, France

Poisson Geometry, Deformation Quantisation and Group Representations

Series: London Mathematical Society Lecture Note Series
Paperback (ISBN-10: 0521615054 )

available from July 2005

Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an introduction to the subject from a small group of leading researchers, and the result is a volume accessible to graduate students or experts from other fields. The contributions are: Poisson Geometry and Morita Equivalence by Bursztyn and Weinstein; Formality and Star Products by Cattaneo; Lie Groupoids, Sheaves and Cohomology by Moerdijk and Mrcun; Geometric Methods in Representation Theory by Schmid; Deformation Theory: A Powerful Tool in Physics Modelling by Sternheimer.

●Presents an introduction to the subject from a small group of leading researchers

● A volume accessible to graduate students or experts from other fields

● Contributions from an array of leading researchers in the field

Contents

1. Poisson geometry and Morita equivalence Henrique Bursztyn and Alan Weinstein; 2. Formality and star products Alberto S. Cattaneo and D. Indelicato; 3. Lie groupoids, sheaves and cohomology; 4. Geometric methods in representation theory Wilfried Schmid and Matvei Libine; 5. Deformation theory: a powerful tool in physics modelling Daniel Sternheimer.

Contributors
Henrique Bursztyn, Alan Weinstein, Alberto S. Cattaneo, D. Indelicato, Wilfried Schmid, Matvei Libine, Daniel Sternheimer