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Books on the topic 'Infinite-Dimensional statistics'

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Author: Grafiati

Published: 1 June 2024

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1

Giné, Evarist. Mathematical foundations of infinite-dimensional statistical models. New York, NY: Cambridge University Press, 2016.

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2

Liu, Kai. Stability of infinite dimensional stochastic differential equations with applications. Boca Raton, FL: Chapman & Hall/CRC, 2006.

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3

Pantsulaia, Gogi. Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces. Hauppauge, N.Y: Nova Science Publishers, 2007.

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4

Socolovsky, Eduardo A. A dissimilarity measure for clustering high- and infinite dimensional data that satisfies the triangle inequality. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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5

Osswald, Horst. Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion: An introduction. Cambridge: Cambridge University Press, 2012.

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6

Accardi, Luigi. Recent Developments in Infinite-Dimensional Analysis and Quantum Probability: Papers in Honour of Takeyuki Hida's 70th Birthday. Dordrecht: Springer Netherlands, 2001.

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7

Conference on Quantum Probability and Infinite Dimensional Analysis (29th 2008 Ḥammāmāt, Tunisia). Quantum probability and infinite dimensional analysis: Proceedings of the 29th conference, Hammamet, Tunisia 13-18 October 2008. New Jersey: World Scientific, 2010.

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8

M, Berezanskiĭ I͡U. Spectral methods in infinite-dimensional analysis. Dordrecht: Kluwer Academic, 1994.

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9

Temam, Roger. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. New York, NY: Springer US, 1988.

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10

Arizona School of Analysis with Applications (2nd 2010 University of Arizona). Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Edited by Sims Robert 1975- and Ueltschi Daniel 1969-. Providence, R.I: American Mathematical Society, 2011.

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11

Gustafson, Karl. Operator Geometry in Statistics. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.13.

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This article discusses the essentials of operator trigonometry developed by the author as it applies to statistics, with emphasis on key elements such as operator antieigenvalues, operator antieigenvectors, and operator turning angles. Operator trigonometry started out infinite dimensional, and remains infinite dimensional, even for Banach spaces. Thus, it is in principle applicable not only to infinite-dimensional statistics but also to cases involving functional data. The article first considers how operator trigonometry gives new geometrical meaning to statistical efficiency before formalizing it in a more deductive manner. It then explains the essentials of operator trigonometry and summarizes the ensuing developments. It also describes two lemmas that are implicit and essential to operator trigonometry, Antieigenvector Reconstruction Lemma and General Two-Component Lemma, and how operator trigonometry provides new geometry to statistics matrix inequalities and canonical correlations. Finally, it presents new results applying operator trigonometry to prediction theory and to association measures.

12

Osswald, Horst. Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion. Cambridge University Press, 2012.

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13

Osswald, Horst. Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion. Cambridge University Press, 2012.

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14

Osswald, Horst. Malliavin Calculus for lévy Processes and Infinite-Dimensional Brownian Motion. Cambridge University Press, 2012.

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15

Ferraty, Frédéric, and Yves Romain, eds. The Oxford Handbook of Functional Data Analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.001.0001.

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This handbook presents the state-of-the-art of the statistics dealing with functional data analysis. With contributions from international experts in the field, it discusses a wide range of the most important statistical topics (classification, inference, factor-based analysis, regression modeling, resampling methods, time series, random processes) while also taking into account practical, methodological, and theoretical aspects of the problems. The book is organised into three sections. Part I deals with regression modeling and covers various statistical methods for functional data such as linear/nonparametric functional regression, varying coefficient models, and linear/nonparametric functional processes (i.e. functional time series). Part II considers related benchmark methods/tools for functional data analysis, including curve registration methods for preprocessing functional data, functional principal component analysis, and resampling/bootstrap methods. Finally, Part III examines some of the fundamental mathematical aspects of the infinite-dimensional setting, with a focus on the stochastic background and operatorial statistics: vector-valued function integration, spectral and random measures linked to stationary processes, operator geometry, vector integration and stochastic integration in Banach spaces, and operatorial statistics linked to quantum statistics.

16

Giné, Evarist, and Richard Nickl. Mathematical Foundations of Infinite-Dimensional Statistical Models. University of Cambridge ESOL Examinations, 2021.

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17

Evarist Giné and Richard Nickl. Mathematical Foundations of Infinite-Dimensional Statistical Models. Cambridge University Press, 2016.

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18

Giné, Evarist, and Richard Nickl. Mathematical Foundations of Infinite-Dimensional Statistical Models. Cambridge University Press, 2015.

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19

Giné, Evarist, and Richard Nickl. Mathematical Foundations of Infinite-Dimensional Statistical Models. University of Cambridge ESOL Examinations, 2021.

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20

Kondratiev, Y. G., Yu M. Berezansky, D. V. Malyshev, and P. V. Malyshev. Spectral Methods in Infinite-Dimensional Analysis. Springer, 2013.

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21

Kondratiev, Y. G., Yu M. Berezansky, D. V. Malyshev, and P. V. Malyshev. Spectral Methods in Infinite-Dimensional Analysis. Springer Netherlands, 2012.

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22

Temam, Roger. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer New York, 2013.

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23

Grenander, Ulf, and Michael I. Miller. Pattern Theory. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198505709.001.0001.

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Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

24

Berezansky, Y. M., and Y. G. Kondratiev. Spectral Methods in Infinite-Dimensional Analysis: Volume I Volume II (Mathematical Physics and Applied Mathematics). Springer, 1995.

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