Random Toeplitz Functionals And Their Applications

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Random Toeplitz Functionals And Their Applications

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Author : Mamikon Ginovian
language : en
Publisher:
Release Date : 2025

Random Toeplitz Functionals And Their Applications written by Mamikon Ginovian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Stochastic models categories.

This book presents recent findings on central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals of stationary processes, with applications in spectral-based statistical inference. It focuses on Gaussian, orthogonal increment-driven, and Lévy-driven linear stationary processes with memory, in both discrete and continuous time. Toeplitz matrices and operators are central to the study of stationary processes. The covariance matrix of a discrete-time stationary process is a truncated Toeplitz matrix generated by the process's spectral density; in continuous-time, this becomes a Toeplitz operator. The foundations of the trace approximation problem were laid by Grenander and Szegö in their classical monograph “Toeplitz Forms and Their Applications” (1958), and the subject has recently seen renewed interest due to developments in long-range dependence and tapered data analysis. The book addresses topics that are often overlooked in other texts, including the trace approximation problem, central limit theorems in continuous time, functional central and non-central limit theorems for Toeplitz processes, and central limit theorems for tapered functionals. It also covers approaches to estimating linear and nonlinear spectral functionals, Whittle estimators, and goodness-of-fit tests using tapered data - each enriched by new advances in the field.

Random Toeplitz Functionals And Their Applications

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Author : Mamikon S. Ginovyan
language : en
Publisher: Springer Nature
Release Date : 2025-11-14

Random Toeplitz Functionals And Their Applications written by Mamikon S. Ginovyan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-11-14 with Mathematics categories.

This book presents recent findings on central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals of stationary processes, with applications in spectral-based statistical inference. It focuses on Gaussian, orthogonal increment-driven, and Lévy-driven linear stationary processes with memory, in both discrete and continuous time. Toeplitz matrices and operators are central to the study of stationary processes. The covariance matrix of a discrete-time stationary process is a truncated Toeplitz matrix generated by the process's spectral density; in continuous-time, this becomes a Toeplitz operator. The foundations of the trace approximation problem were laid by Grenander and Szegö in their classical monograph “Toeplitz Forms and Their Applications” (1958), and the subject has recently seen renewed interest due to developments in long-range dependence and tapered data analysis. The book addresses topics that are often overlooked in other texts, including the trace approximation problem, central limit theorems in continuous time, functional central and non-central limit theorems for Toeplitz processes, and central limit theorems for tapered functionals. It also covers approaches to estimating linear and nonlinear spectral functionals, Whittle estimators, and goodness-of-fit tests using tapered data – each enriched by new advances in the field. Comprising ten chapters and two appendices, the book begins with an overview of the main problems and a review of foundational concepts from real analysis, functional analysis, and matrix analysis. It then introduces a model that is a second-order stationary process and discusses key concepts and results from the general theory of stationary processes, before delving into the trace approximation problem. Subsequent chapters cover central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals and explore statistical inference problems. The appendices discuss the motivations and benefits of data tapering, and outline several important problems closely related to the main themes of the book. The text will be a valuable resource for researchers in time series analysis, econometrics, finance, and applied statistics. It is suitable for graduate-level courses in time series analysis or the statistics of stochastic processes, and as a supplementary reference for students of advanced statistics, probability, econometrics, or finance.

Random Toeplitz Functionals And Their Applications

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Author : Mamikon S. Ginovyan
language : en
Publisher: Springer
Release Date : 2025-10-09

Random Toeplitz Functionals And Their Applications written by Mamikon S. Ginovyan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-10-09 with Mathematics categories.

This book presents recent findings on central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals of stationary processes, with applications in spectral-based statistical inference. It focuses on Gaussian, orthogonal increment-driven, and Lévy-driven linear stationary processes with memory, in both discrete and continuous time. Toeplitz matrices and operators are central to the study of stationary processes. The covariance matrix of a discrete-time stationary process is a truncated Toeplitz matrix generated by the process's spectral density; in continuous-time, this becomes a Toeplitz operator. The foundations of the trace approximation problem were laid by Grenander and Szegö in their classical monograph “Toeplitz Forms and Their Applications” (1958), and the subject has recently seen renewed interest due to developments in long-range dependence and tapered data analysis. The book addresses topics that are often overlooked in other texts, including the trace approximation problem, central limit theorems in continuous time, functional central and non-central limit theorems for Toeplitz processes, and central limit theorems for tapered functionals. It also covers approaches to estimating linear and nonlinear spectral functionals, Whittle estimators, and goodness-of-fit tests using tapered data – each enriched by new advances in the field. Comprising ten chapters and two appendices, the book begins with an overview of the main problems and a review of foundational concepts from real analysis, functional analysis, and matrix analysis. It then introduces a model that is a second-order stationary process and discusses key concepts and results from the general theory of stationary processes, before delving into the trace approximation problem. Subsequent chapters cover central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals and explore statistical inference problems. The appendices discuss the motivations and benefits of data tapering, and outline several important problems closely related to the main themes of the book. The text will be a valuable resource for researchers in time series analysis, econometrics, finance, and applied statistics. It is suitable for graduate-level courses in time series analysis or the statistics of stochastic processes, and as a supplementary reference for students of advanced statistics, probability, econometrics, or finance.

Computing And Combinatorics

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Author : Ding-Zhu Du
language : en
Publisher: Springer
Release Date : 2013-05-17

Computing And Combinatorics written by Ding-Zhu Du and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-17 with Computers categories.

This book constitutes the refereed proceedings of the 19th International Conference on Computing and Combinatorics, COCOON 2013, held in Hangzhou, China, in June 2013. The 56 revised full papers presented were carefully reviewed and selected from 120 submissions. There was a co-organized workshop on discrete algorithms of which 8 short papers were accepted and a workshop on computational social networks where 12 papers out of 25 submissions were accepted.

Oar Index Of Research Results

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Author :
language : en
Publisher:
Release Date : 1967

Oar Index Of Research Results written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Aeronautics categories.

Oar Quarterly Index Of Current Research Results

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Author : United States. Air Force. Office of Aerospace Research
language : en
Publisher:
Release Date : 1967

Oar Quarterly Index Of Current Research Results written by United States. Air Force. Office of Aerospace Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Aeronautics, Military categories.

Special Topics In Structural Dynamics Volume 6

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Author : Randall Allemang
language : en
Publisher: CRC Press
Release Date : 2025-08-07

Special Topics In Structural Dynamics Volume 6 written by Randall Allemang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-07 with Technology & Engineering categories.

Special Topics in Structural Dynamics, Volume 6: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the sixth volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Teaching Experimental & Analytical Structural Dynamics Sensors & Instrumentation Aircraft/Aerospace Bio-Dynamics Sports Equipment Dynamics Advanced ODS & Stress Estimation Shock & Vibration Full-Field Optical Measurements & Image Analysis Structural Health Monitoring Operational Modal Analysis Wind Turbine Dynamics Rotating Machinery Finite Element Methods Energy Harvesting.

National Symposium On Functional Analysis Optimization And Applications

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Author : John R. Giles
language : en
Publisher:
Release Date : 1999

National Symposium On Functional Analysis Optimization And Applications written by John R. Giles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Functional analysis categories.

Oar Index Of Research Results

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Author : United States. Air Force. Office of Aerospace Research
language : en
Publisher:
Release Date : 1967

Oar Index Of Research Results written by United States. Air Force. Office of Aerospace Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Current Index To Statistics Applications Methods And Theory

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Author :
language : en
Publisher:
Release Date : 1994

Current Index To Statistics Applications Methods And Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematical statistics categories.

The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.