Statistical Inference For Discrete Time Stochastic Processes

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Statistical Inference for Discrete Time Stochastic Processes

M. B. Rajarshi
Statistical Inference for Discrete Time Stochastic Processes Book PDF

Author : M. B. Rajarshi
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 53,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9788132207634

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Statistical Inference for Discrete Time Stochastic Processes by M. B. Rajarshi Pdf

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

Denis Bosq,Hung T. Nguyen
A Course in Stochastic Processes Book PDF

Author : Denis Bosq,Hung T. Nguyen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401587693

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A Course in Stochastic Processes by Denis Bosq,Hung T. Nguyen Pdf

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

Lyle D. Broemeling
Bayesian Inference for Stochastic Processes Book PDF

Author : Lyle D. Broemeling
Publisher : CRC Press
Page : 373 pages
File Size : 42,9 Mb
Release : 2017-12-12
Category : Mathematics
ISBN : 9781315303574

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Bayesian Inference for Stochastic Processes by Lyle D. Broemeling Pdf

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 in Stochastic Processes

N.U. Prabhu
Statistical Inference in Stochastic Processes Book PDF

Author : N.U. Prabhu
Publisher : CRC Press
Page : 294 pages
File Size : 45,9 Mb
Release : 2020-08-13
Category : Mathematics
ISBN : 9781000147742

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Statistical Inference in Stochastic Processes by N.U. Prabhu Pdf

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 Inference from Stochastic Processes

Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie,Narahari Umanath Prabhu,Joint Summer Research Conference in the Mathematical Sciences on Statistical Inference from Stochastic Processes (1987, Ithaca, NY),AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE IN T
Statistical Inference from Stochastic Processes Book PDF

Author : Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie,Narahari Umanath Prabhu,Joint Summer Research Conference in the Mathematical Sciences on Statistical Inference from Stochastic Processes (1987, Ithaca, NY),AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE IN T
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 43,7 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850879

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Statistical Inference from Stochastic Processes by Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie,Narahari Umanath Prabhu,Joint Summer Research Conference in the Mathematical Sciences on Statistical Inference from Stochastic Processes (1987, Ithaca, NY),AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE IN T Pdf

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.

Statistical Inferences for Stochasic Processes

Ishwar V. Basawa
Statistical Inferences for Stochasic Processes Book PDF

Author : Ishwar V. Basawa
Publisher : Elsevier
Page : 435 pages
File Size : 43,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483296142

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Statistical Inferences for Stochasic Processes by Ishwar V. Basawa Pdf

Stats Inference Stochasic Process

Point Processes and Their Statistical Inference

Alan Karr
Point Processes and Their Statistical Inference Book PDF

Author : Alan Karr
Publisher : Routledge
Page : 577 pages
File Size : 48,9 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351423823

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Point Processes and Their Statistical Inference by Alan Karr Pdf

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

Statistical Inferences for Stochasic Processes

Ishwar V. Basawa,B. L. S. Prakasa Rao
Statistical Inferences for Stochasic Processes Book PDF

Author : Ishwar V. Basawa,B. L. S. Prakasa Rao
Publisher : Academic Press
Page : 464 pages
File Size : 41,9 Mb
Release : 1980-01-28
Category : Mathematics
ISBN : UOM:39015006420015

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Statistical Inferences for Stochasic Processes by Ishwar V. Basawa,B. L. S. Prakasa Rao Pdf

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

Statistical Inference for Diffusion Type Processes

B.L.S. Prakasa Rao
Statistical Inference for Diffusion Type Processes Book PDF

Author : B.L.S. Prakasa Rao
Publisher : Wiley
Page : 0 pages
File Size : 52,9 Mb
Release : 2010-05-24
Category : Mathematics
ISBN : 0470711124

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Statistical Inference for Diffusion Type Processes by B.L.S. Prakasa Rao Pdf

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.

Asymptotic Theory of Statistical Inference for Time Series

Masanobu Taniguchi,Yoshihide Kakizawa
Asymptotic Theory of Statistical Inference for Time Series Book PDF

Author : Masanobu Taniguchi,Yoshihide Kakizawa
Publisher : Springer Science & Business Media
Page : 671 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211624

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Asymptotic Theory of Statistical Inference for Time Series by Masanobu Taniguchi,Yoshihide Kakizawa Pdf

The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Probability, Statistics, and Stochastic Processes

Peter Olofsson
Probability Statistics and Stochastic Processes Book PDF

Author : Peter Olofsson
Publisher : John Wiley & Sons
Page : 500 pages
File Size : 48,9 Mb
Release : 2011-07-20
Category : Mathematics
ISBN : 9780471743057

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Probability, Statistics, and Stochastic Processes by Peter Olofsson Pdf

A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation. Also included is a chapter on statistical inference with a section on Bayesian statistics, which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time are also discussed within the book. More than 400 examples are interspersed throughout the text to help illustrate concepts and theory and to assist the reader in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter. This book is an excellent text for upper-level undergraduate courses. While many texts treat probability theory and statistical inference or probability theory and stochastic processes, this text enables students to become proficient in all three of these essential topics. For students in science and engineering who may take only one course in probability theory, mastering all three areas will better prepare them to collect, analyze, and characterize data in their chosen fields.

Nonparametric Statistics for Stochastic Processes

Denis Bosq
Nonparametric Statistics for Stochastic Processes Book PDF

Author : Denis Bosq
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468404890

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Nonparametric Statistics for Stochastic Processes by Denis Bosq Pdf

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.

Probability and Statistical Inference

Miltiadis C. Mavrakakis,Jeremy Penzer
Probability and Statistical Inference Book PDF

Author : Miltiadis C. Mavrakakis,Jeremy Penzer
Publisher : CRC Press
Page : 444 pages
File Size : 42,6 Mb
Release : 2021-03-28
Category : Mathematics
ISBN : 9781315362045

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Probability and Statistical Inference by Miltiadis C. Mavrakakis,Jeremy Penzer Pdf

Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting. Features: •Complete introduction to mathematical probability, random variables, and distribution theory. •Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes. •Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference. •Detailed introduction to Bayesian statistics and associated topics. •Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC). This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.

Probability & Statistics With Reliability, Queuing And Computer Science Applications, 2Nd Ed

Kishor S. Trivedi
Probability Statistics With Reliability Queuing And Computer Science Applications 2Nd Ed Book PDF

Author : Kishor S. Trivedi
Publisher : John Wiley & Sons
Page : 852 pages
File Size : 41,6 Mb
Release : 2008-10-15
Category : Electronic
ISBN : 8126518537

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Probability & Statistics With Reliability, Queuing And Computer Science Applications, 2Nd Ed by Kishor S. Trivedi Pdf

This book is important to our developing list of computer science titles. Trivedi's book is a true classic and will be well received in the market. The subject lies at the core of many applications in computer science, signal processing, and communications. · Introduction· Discrete Random Variables· Continuous Random Variables· Expectation· Conditional Distribution and Expectation· Stochastic Processes· Discrete-Time Markov Chains· Continuous-Time Markov Chains· Networks of Queues· Statistical Inference · Regression and Analysis of Variance

Theory of Stochastic Objects

Athanasios Christou Micheas
Theory of Stochastic Objects Book PDF

Author : Athanasios Christou Micheas
Publisher : CRC Press
Page : 409 pages
File Size : 41,6 Mb
Release : 2018-01-19
Category : Mathematics
ISBN : 9781466515215

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Theory of Stochastic Objects by Athanasios Christou Micheas Pdf

This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete. Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics. Includes 378 exercises, with the solutions manual available on the book's website. 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example). The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.