Ebook: Linear Processes in Function Spaces: Theory and Applications

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.
The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).

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The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.
The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).

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The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.
The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).
Content:
Front Matter....Pages i-xiii
Synopsis....Pages 1-14
Stochastic Processes and Random Variables in Function Spaces....Pages 15-42
Sequences of Random Variables in Banach Spaces....Pages 43-70
Autoregressive Hilbertian Processes of Order 1....Pages 71-94
Estimation of Autocovariance Operators for ARH(1) Processes....Pages 95-125
Autoregressive Hilbertian Processes of Order p ....Pages 127-145
Autoregressive Processes in Banach Spaces....Pages 147-180
General Linear Processes in Function Spaces....Pages 181-202
Estimation of Autocorrelation Operator and Prediction....Pages 203-236
Implementation of Functional Autoregressive Predictors and Numerical Applications....Pages 237-261
Back Matter....Pages 263-286

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The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.
The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).
Content:
Front Matter....Pages i-xiii
Synopsis....Pages 1-14
Stochastic Processes and Random Variables in Function Spaces....Pages 15-42
Sequences of Random Variables in Banach Spaces....Pages 43-70
Autoregressive Hilbertian Processes of Order 1....Pages 71-94
Estimation of Autocovariance Operators for ARH(1) Processes....Pages 95-125
Autoregressive Hilbertian Processes of Order p ....Pages 127-145
Autoregressive Processes in Banach Spaces....Pages 147-180
General Linear Processes in Function Spaces....Pages 181-202
Estimation of Autocorrelation Operator and Prediction....Pages 203-236
Implementation of Functional Autoregressive Predictors and Numerical Applications....Pages 237-261
Back Matter....Pages 263-286
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