Mathematical Foundations Of Infinite Dimensional Statistical Models

Author : Evarist Giné
Publisher : Cambridge University Press
ISBN 13 : 1009022784
Total Pages : 706 pages
Book Rating : 4.81/5 ( download)

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Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.

Author : Martin J. Wainwright
Publisher : Cambridge University Press
ISBN 13 : 1108498027
Total Pages : 571 pages
Book Rating : 4.29/5 ( download)

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Download or read book High-Dimensional Statistics written by Martin J. Wainwright and published by Cambridge University Press. This book was released on 2019-02-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Author : Jayakrishnan Nair
Publisher : Cambridge University Press
ISBN 13 : 1009062964
Total Pages : 266 pages
Book Rating : 4.61/5 ( download)

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Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.

Author : Michael P. Fay
Publisher : Cambridge University Press
ISBN 13 : 1108423566
Total Pages : 449 pages
Book Rating : 4.64/5 ( download)

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Download or read book Statistical Hypothesis Testing in Context written by Michael P. Fay and published by Cambridge University Press. This book was released on 2022-05-05 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent guide equips applied statisticians to make good choices and proper interpretations in real investigations facing real data.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 1316805581
Total Pages : 508 pages
Book Rating : 4.89/5 ( download)

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Download or read book Random Graphs and Complex Networks: Volume 2 written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2024-02-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

Author : Charles Bouveyron
Publisher : Cambridge University Press
ISBN 13 : 110849420X
Total Pages : 446 pages
Book Rating : 4.05/5 ( download)

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Download or read book Model-Based Clustering and Classification for Data Science written by Charles Bouveyron and published by Cambridge University Press. This book was released on 2019-07-25 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Colorful example-rich introduction to the state-of-the-art for students in data science, as well as researchers and practitioners.

Author : Sébastien Roch
Publisher : Cambridge University Press
ISBN 13 : 1009305131
Total Pages : 452 pages
Book Rating : 4.36/5 ( download)

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Download or read book Modern Discrete Probability written by Sébastien Roch and published by Cambridge University Press. This book was released on 2024-01-18 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.

Author : Donald B. Percival
Publisher : Cambridge University Press
ISBN 13 : 1108776175
Total Pages : 718 pages
Book Rating : 4.72/5 ( download)

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Download or read book Spectral Analysis for Univariate Time Series written by Donald B. Percival and published by Cambridge University Press. This book was released on 2020-03-19 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book's website.

Author : Subhashis Ghosal
Publisher : Cambridge University Press
ISBN 13 : 1108210120
Total Pages : 671 pages
Book Rating : 4.26/5 ( download)

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Download or read book Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by Cambridge University Press. This book was released on 2017-06-26 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.

Author : Nihat Ay
Publisher : Springer
ISBN 13 : 3319564781
Total Pages : 407 pages
Book Rating : 4.84/5 ( download)

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Download or read book Information Geometry written by Nihat Ay and published by Springer. This book was released on 2017-08-25 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.