Statistical Inference For Discrete Time Stochastic Processes


Statistical Inference For Discrete Time Stochastic Processes
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Statistical Inference For Discrete Time Stochastic Processes


Statistical Inference For Discrete Time Stochastic Processes
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Author : M. B. Rajarshi
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08

Statistical Inference For Discrete Time Stochastic Processes written by M. B. Rajarshi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.


This work is an overview of statistical inference in stationary, discrete time stochastic processes. Results in the last fifteen years, particularly on non-Gaussian sequences and semi-parametric and non-parametric analysis have been reviewed. The first chapter gives a background of results on martingales and strong mixing sequences, which enable us to generate various classes of CAN estimators in the case of dependent observations. Topics discussed include inference in Markov chains and extension of Markov chains such as Raftery's Mixture Transition Density model and Hidden Markov chains and extensions of ARMA models with a Binomial, Poisson, Geometric, Exponential, Gamma, Weibull, Lognormal, Inverse Gaussian and Cauchy as stationary distributions. It further discusses applications of semi-parametric methods of estimation such as conditional least squares and estimating functions in stochastic models. Construction of confidence intervals based on estimating functions is discussed in some detail. Kernel based estimation of joint density and conditional expectation are also discussed. Bootstrap and other resampling procedures for dependent sequences such as Markov chains, Markov sequences, linear auto-regressive moving average sequences, block based bootstrap for stationary sequences and other block based procedures are also discussed in some detail. This work can be useful for researchers interested in knowing developments in inference in discrete time stochastic processes. It can be used as a material for advanced level research students.



A Course In Stochastic Processes


A Course In Stochastic Processes
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Author : Denis Bosq
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

A Course In Stochastic Processes written by Denis Bosq and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.


This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math ematically?". The exercises at the end of each lesson will deepen the stu dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.



Bayesian Inference For Stochastic Processes


Bayesian Inference For Stochastic Processes
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Author : Lyle D. Broemeling
language : en
Publisher: CRC Press
Release Date : 2017-12-12

Bayesian Inference For Stochastic Processes written by Lyle D. Broemeling and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-12 with Mathematics categories.


This is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter devoted to the fundamental concepts in stochastic processes is included. Bayesian inference (estimation, testing hypotheses, and prediction) for discrete time Markov chains, for Markov jump processes, for normal processes (e.g. Brownian motion and the Ornstein–Uhlenbeck process), for traditional time series, and, lastly, for point and spatial processes are described in detail. Heavy emphasis is placed on many examples taken from biology and other scientific disciplines. In order analyses of stochastic processes, it will use R and WinBUGS. Features: Uses the Bayesian approach to make statistical Inferences about stochastic processes The R package is used to simulate realizations from different types of processes Based on realizations from stochastic processes, the WinBUGS package will provide the Bayesian analysis (estimation, testing hypotheses, and prediction) for the unknown parameters of stochastic processes To illustrate the Bayesian inference, many examples taken from biology, economics, and astronomy will reinforce the basic concepts of the subject A practical approach is implemented by considering realistic examples of interest to the scientific community WinBUGS and R code are provided in the text, allowing the reader to easily verify the results of the inferential procedures found in the many examples of the book Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.



Statistical Inference For Diffusion Type Processes


Statistical Inference For Diffusion Type Processes
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Author : B.L.S. Prakasa Rao
language : en
Publisher: Wiley
Release Date : 2010-05-24

Statistical Inference For Diffusion Type Processes written by B.L.S. Prakasa Rao and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-24 with Mathematics categories.


Decision making in all spheres of activity involves uncertainty. If rational decisions have to be made, they have to be based on the past observations of the phenomenon in question. Data collection, model building and inference from the data collected, validation of the model and refinement of the model are the key steps or building blocks involved in any rational decision making process. Stochastic processes are widely used for model building in the social, physical, engineering, and life sciences as well as in financial economics. Statistical inference for stochastic processes is of great importance from the theoretical as well as from applications point of view in model building. During the past twenty years, there has been a large amount of progress in the study of inferential aspects for continuous as well as discrete time stochastic processes. Diffusion type processes are a large class of continuous time processes which are widely used for stochastic modelling. the book aims to bring together several methods of estimation of parameters involved in such processes when the process is observed continuously over a period of time or when sampled data is available as generally feasible.



Nonparametric Statistics For Stochastic Processes


Nonparametric Statistics For Stochastic Processes
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Author : Denis Bosq
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonparametric Statistics For Stochastic Processes written by Denis Bosq and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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 Inference In Stochastic Processes


Statistical Inference In Stochastic Processes
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Author : N.U. Prabhu
language : en
Publisher: CRC Press
Release Date : 2020-08-13

Statistical Inference In Stochastic Processes written by N.U. Prabhu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-13 with Mathematics categories.


Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di



Statistical Inferences For Stochasic Processes


Statistical Inferences For Stochasic Processes
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Author : Ishwar V. Basawa
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Statistical Inferences For Stochasic Processes written by Ishwar V. Basawa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.


Stats Inference Stochasic Process



Statistical Inference From Stochastic Processes


Statistical Inference From Stochastic Processes
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Author : Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Statistical Inference From Stochastic Processes written by Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.


This volume comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. The conference brought together probabilists and statisticians who have developed important areas of application and made major contributions to the foundations of the subject. Statistical inference from stochastic processes has been important in a number of areas. For example, in applied probability, major advances have been made in recent years in stochastic models arising in science and engineering. However, the emphasis has been on the formulation and analysis of models rather than on the statistical methodology for hypothesis testing and inference. For these models to be of practical use, procedures for their statistical analysis are essential. In the area of probability models, initial work in inference focused on Markov chains, but many models have given rise to non-Markovian and point processes. In recent years, research in statistical inference from such processes not only solved specific problems but also resulted in major contributions to the conceptual framework of the subject as well as the associated techniques. The objective of the conference was to provide the opportunity to survey and evaluate the current state of the art in this area and to discuss future directions. The papers presented covered five topics within the broad domain of inference from stochastic processes: foundations, counting processes and survival analysis, likelihood and its ramifications, applications to statistics and probability models, and processes in economics. Requiring a graduate level background in probability and statistical inference, this book will provide students and researchers with a familiarity with the foundations of inference from stochastic processes and a knowledge of the current developments in this area.



Point Processes And Their Statistical Inference


Point Processes And Their Statistical Inference
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Author : Alan Karr
language : en
Publisher: Routledge
Release Date : 2017-09-06

Point Processes And Their Statistical Inference written by Alan Karr and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.


First Published in 2017. Routledge is an imprint of Taylor & Francis, an Informa company.



Statistical Inferences For Stochasic Processes


Statistical Inferences For Stochasic Processes
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Author : Ishwar V. Basawa
language : en
Publisher: Academic Press
Release Date : 1980-01-28

Statistical Inferences For Stochasic Processes written by Ishwar V. Basawa and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-28 with Mathematics categories.


Introductory examples of stochastic models; Special models; General theory; Further approaches.