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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous ...
Challenges For The 21st Century, Procs Of The Intl Conf On Fundamental Sciences: Mathematics And Theoretical Physics
The International Conference on Fundamental Sciences: Mathematics and Theoretical Physics provided a forum for reviewing some of the significant developments in mathematics and theoretical physics in the 20th century; for the leading theorists in these fields to expound and discuss their views on new ideas and trends in the basic sciences as the new millennium approached; for increasing public awareness of the importance of basic research in mathematics and theoretical physics; and for promoting a high level of interest in mathematics and theoretical physics among school students and teachers. This was a major conference, with invited lectures by some of the leading experts in various fields of mathematics and theoretical physics.
Asymptotic Properties of Permanental Sequences
This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.
Non-Gaussian Selfsimilar Stochastic Processes
This book offers an introduction to the field of stochastic analysis of Hermite processes. These selfsimilar stochastic processes with stationary increments live in a Wiener chaos and include the fractional Brownian motion, the only Gaussian process in this class. Using the Wiener chaos theory and multiple stochastic integrals, the book covers the main properties of Hermite processes and their multiparameter counterparts, the Hermite sheets. It delves into the probability distribution of these stochastic processes and their sample paths, while also presenting the basics of stochastic integration theory with respect to Hermite processes and sheets. The book goes beyond theory and provides a thorough analysis of physical models driven by Hermite noise, including the Hermite Ornstein-Uhlenbeck process and the solution to the stochastic heat equation driven by such a random perturbation. Moreover, it explores up-to-date topics central to current research in statistical inference for Hermite-driven models.
Theory and Applications of Long-Range Dependence
The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject. The topics selected should give a good overview from the prob...
Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference
This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors.
Statistical Analysis of Extreme Values
This is a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values, as used in disciplines from hydrology to finance to environmental science. Updated and expanded by 100 pages.
An Invitation to Statistics in Wasserstein Space
This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satis...
Peterson's Graduate Programs in the Physical Sciences, Mathematics, Agricultural Sciences, the Environment & Natural Resources 2012
Graduate Programs in the Physical Sciences, Mathematics, Agricultural Sciences, the Environment & Natural Resources 2012 contains more than 2,900 graduate programs in 59 disciplines-including agriculture and food sciences, astronomy and astrophysics, chemistry, physics, mathematics, environmental sciences and management, natural resources, marine sciences, and more. This guide is part of Peterson's six-volume Annual Guides to Graduate Study, the only annually updated reference work of its kind, provides wide-ranging information on the graduate and professional programs offered by U.S.-accredited colleges and universities in the United States and throughout the world. Informative data profile...
Challenges for the 21st Century
The International Conference on Fundamental Sciences: Mathematics and Theoretical Physics provided a forum for reviewing some of the significant developments in mathematics and theoretical physics in the 20th century; for the leading theorists in these fields to expound and discuss their views on new ideas and trends in the basic sciences as the new millennium approached; for increasing public awareness of the importance of basic research in mathematics and theoretical physics; and for promoting a high level of interest in mathematics and theoretical physics among school students and teachers. This was a major conference, with invited lectures by some of the leading experts in various fields of mathematics and theoretical physics.
