Author: Mikhail Moklyachuk
Publisher:
ISBN: 9781536158908
Category : Missing observations (Statistics)
Languages : en
Pages : 0
Book Description
We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.
Estimation of Stochastic Processes with Missing Observations
Author: Mikhail Moklyachuk
Publisher:
ISBN: 9781536158908
Category : Missing observations (Statistics)
Languages : en
Pages : 0
Book Description
We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.
Publisher:
ISBN: 9781536158908
Category : Missing observations (Statistics)
Languages : en
Pages : 0
Book Description
We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.
Nonparametric Statistics for Stochastic Processes
Author: Denis Bosq
Publisher: Springer Science & Business Media
ISBN: 146840489X
Category : Mathematics
Languages : en
Pages : 181
Book Description
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.
Publisher: Springer Science & Business Media
ISBN: 146840489X
Category : Mathematics
Languages : en
Pages : 181
Book Description
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.
Statistical Estimation for Stochastic Processes
Author: K. Nanthi
Publisher: Kingston, Ont. : Queen's University
ISBN:
Category : Estimation theory
Languages : en
Pages : 286
Book Description
Publisher: Kingston, Ont. : Queen's University
ISBN:
Category : Estimation theory
Languages : en
Pages : 286
Book Description
Stochastic Processes
Author: Kaddour Najim
Publisher: Elsevier
ISBN: 008051779X
Category : Mathematics
Languages : en
Pages : 345
Book Description
A 'stochastic' process is a 'random' or 'conjectural' process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.This book deals with the tools and techniques used in the stochastic process – estimation, optimisation and recursive logarithms – in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.*An engineering approach to applied probabilities and statistics *Presents examples related to practical engineering applications, such as reliability, randomness and use of resources*Readers with varying interests and mathematical backgrounds will find this book accessible
Publisher: Elsevier
ISBN: 008051779X
Category : Mathematics
Languages : en
Pages : 345
Book Description
A 'stochastic' process is a 'random' or 'conjectural' process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.This book deals with the tools and techniques used in the stochastic process – estimation, optimisation and recursive logarithms – in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.*An engineering approach to applied probabilities and statistics *Presents examples related to practical engineering applications, such as reliability, randomness and use of resources*Readers with varying interests and mathematical backgrounds will find this book accessible
Statistical Analysis of Stochastic Processes in Time
Author: J. K. Lindsey
Publisher: Cambridge University Press
ISBN: 9781139454513
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
Publisher: Cambridge University Press
ISBN: 9781139454513
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
Statistical Inferences for Stochasic Processes
Author: Ishwar V. Basawa
Publisher: Academic Press
ISBN:
Category : Mathematics
Languages : en
Pages : 464
Book Description
Introductory examples of stochastic models; Special models; General theory; Further approaches.
Publisher: Academic Press
ISBN:
Category : Mathematics
Languages : en
Pages : 464
Book Description
Introductory examples of stochastic models; Special models; General theory; Further approaches.
Statistical Estimation for Imperfectly-observed Stochastic Processes
Statistical Inference from Stochastic Processes
Author: Narahari Umanath Prabhu
Publisher: American Mathematical Soc.
ISBN: 0821850873
Category : Mathematics
Languages : en
Pages : 406
Book Description
Comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. This book provides students and researchers with a familiarity with the foundations of inference from stochastic processes and intends to provide a knowledge of the developments.
Publisher: American Mathematical Soc.
ISBN: 0821850873
Category : Mathematics
Languages : en
Pages : 406
Book Description
Comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. This book provides students and researchers with a familiarity with the foundations of inference from stochastic processes and intends to provide a knowledge of the developments.
Theory and Statistical Applications of Stochastic Processes
Author: Yuliya Mishura
Publisher: John Wiley & Sons
ISBN: 1119476631
Category : Mathematics
Languages : en
Pages : 406
Book Description
This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.
Publisher: John Wiley & Sons
ISBN: 1119476631
Category : Mathematics
Languages : en
Pages : 406
Book Description
This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.
Statistical Estimation for Stochastic Processes
Author: K. Nanthi
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 245
Book Description
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 245
Book Description