Statistical Inference for Fractional Diffusion Processes
Statistical Inference for Fractional Diffusion Processes

Author: B. L. S. Prakasa Rao

Publisher: John Wiley & Sons

Published: 2011-07-05

Total Pages: 213

ISBN-13: 0470975768

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Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable. Key features: Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion. Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence. Presents a study of parametric and nonparametric inference problems for the fractional diffusion process. Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion. Includes recent results and developments in the area of statistical inference of fractional diffusion processes. Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.

Parameter Estimation in Fractional Diffusion Models
Parameter Estimation in Fractional Diffusion Models

Author: Kęstutis Kubilius

Publisher: Springer

Published: 2018-01-04

Total Pages: 403

ISBN-13: 3319710303

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This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Applied Linear Regression
Applied Linear Regression

Author: Sanford Weisberg

Publisher: John Wiley & Sons

Published: 2013-11-25

Total Pages: 284

ISBN-13: 1118594851

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Praise for the Third Edition "...this is an excellent book which could easily be used as a course text..." —International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illustrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. While maintaining the accessible appeal of each previous edition,Applied Linear Regression, Fourth Edition features: Graphical methods stressed in the initial exploratory phase, analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple and complex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, and variance assumptions Updated methodology, such as bootstrapping, cross-validation binomial and Poisson regression, and modern model selection methods Applied Linear Regression, Fourth Edition is an excellent textbook for upper-undergraduate and graduate-level students, as well as an appropriate reference guide for practitioners and applied statisticians in engineering, business administration, economics, and the social sciences.

Introduction to Time Series Analysis and Forecasting
Introduction to Time Series Analysis and Forecasting

Author: Douglas C. Montgomery

Publisher: John Wiley & Sons

Published: 2015-04-27

Total Pages: 670

ISBN-13: 1118745116

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Praise for the First Edition "...[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both popular and modern time series methodologies as well as an introduction to Bayesian methods in forecasting. Introduction to Time Series Analysis and Forecasting, Second Edition also includes: Over 300 exercises from diverse disciplines including health care, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®, and R that illustrate the theory and practicality of forecasting techniques in the context of time-oriented data New material on frequency domain and spatial temporal data analysis Expanded coverage of the variogram and spectrum with applications as well as transfer and intervention model functions A supplementary website featuring PowerPoint® slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, Second Edition is an ideal textbook upper-undergraduate and graduate-levels courses in forecasting and time series. The book is also an excellent reference for practitioners and researchers who need to model and analyze time series data to generate forecasts.

Statistical Shape Analysis
Statistical Shape Analysis

Author: Ian L. Dryden

Publisher: John Wiley & Sons

Published: 2016-07-08

Total Pages: 496

ISBN-13: 1119072514

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A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis .

Sample Size Determination and Power
Sample Size Determination and Power

Author: Thomas P. Ryan

Publisher: John Wiley & Sons

Published: 2013-05-28

Total Pages: 230

ISBN-13: 1118439228

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A comprehensive approach to sample size determination and power with applications for a variety of fields Sample Size Determination and Power features a modern introduction to the applicability of sample size determination and provides a variety of discussions on broad topics including epidemiology, microarrays, survival analysis and reliability, design of experiments, regression, and confidence intervals. The book distinctively merges applications from numerous fields such as statistics, biostatistics, the health sciences, and engineering in order to provide a complete introduction to the general statistical use of sample size determination. Advanced topics including multivariate analysis, clinical trials, and quality improvement are addressed, and in addition, the book provides considerable guidance on available software for sample size determination. Written by a well-known author who has extensively class-tested the material, Sample Size Determination and Power: Highlights the applicability of sample size determination and provides extensive literature coverage Presents a modern, general approach to relevant software to guide sample size determination including CATD (computer-aided trial design) Addresses the use of sample size determination in grant proposals and provides up-to-date references for grant investigators An appealing reference book for scientific researchers in a variety of fields, such as statistics, biostatistics, the health sciences, mathematics, ecology, and geology, who use sampling and estimation methods in their work, Sample Size Determination and Power is also an ideal supplementary text for upper-level undergraduate and graduate-level courses in statistical sampling.

Introduction to Linear Regression Analysis
Introduction to Linear Regression Analysis

Author: Douglas C. Montgomery

Publisher: John Wiley & Sons

Published: 2021-03-16

Total Pages: 706

ISBN-13: 1119578728

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INTRODUCTION TO LINEAR REGRESSION ANALYSIS A comprehensive and current introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, 6th Edition is the most comprehensive, fulsome, and current examination of the foundations of linear regression analysis. Fully updated in this new sixth edition, the distinguished authors have included new material on generalized regression techniques and new examples to help the reader understand retain the concepts taught in the book. The new edition focuses on four key areas of improvement over the fifth edition: New exercises and data sets New material on generalized regression techniques The inclusion of JMP software in key areas Carefully condensing the text where possible Introduction to Linear Regression Analysis skillfully blends theory and application in both the conventional and less common uses of regression analysis in today’s cutting-edge scientific research. The text equips readers to understand the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.

Clinical Trial Design
Clinical Trial Design

Author: Guosheng Yin

Publisher: John Wiley & Sons

Published: 2013-06-07

Total Pages: 368

ISBN-13: 1118183320

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A balanced treatment of the theories, methodologies, and design issues involved in clinical trials using statistical methods There has been enormous interest and development in Bayesian adaptive designs, especially for early phases of clinical trials. However, for phase III trials, frequentist methods still play a dominant role through controlling type I and type II errors in the hypothesis testing framework. From practical perspectives, Clinical Trial Design: Bayesian and Frequentist Adaptive Methods provides comprehensive coverage of both Bayesian and frequentist approaches to all phases of clinical trial design. Before underpinning various adaptive methods, the book establishes an overview of the fundamentals of clinical trials as well as a comparison of Bayesian and frequentist statistics. Recognizing that clinical trial design is one of the most important and useful skills in the pharmaceutical industry, this book provides detailed discussions on a variety of statistical designs, their properties, and operating characteristics for phase I, II, and III clinical trials as well as an introduction to phase IV trials. Many practical issues and challenges arising in clinical trials are addressed. Additional topics of coverage include: Risk and benefit analysis for toxicity and efficacy trade-offs Bayesian predictive probability trial monitoring Bayesian adaptive randomization Late onset toxicity and response Dose finding in drug combination trials Targeted therapy designs The author utilizes cutting-edge clinical trial designs and statistical methods that have been employed at the world's leading medical centers as well as in the pharmaceutical industry. The software used throughout the book is freely available on the book's related website, equipping readers with the necessary tools for designing clinical trials. Clinical Trial Design is an excellent book for courses on the topic at the graduate level. The book also serves as a valuable reference for statisticians and biostatisticians in the pharmaceutical industry as well as for researchers and practitioners who design, conduct, and monitor clinical trials in their everyday work.

Understanding Uncertainty
Understanding Uncertainty

Author: Dennis V. Lindley

Publisher: John Wiley & Sons

Published: 2013-11-26

Total Pages: 434

ISBN-13: 1118650239

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Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty." —Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession A consideration of betting, showing that a bookmaker's odds are not expressions of probability Applications of the book’s thesis to statistics A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.

High-Dimensional Covariance Estimation
High-Dimensional Covariance Estimation

Author: Mohsen Pourahmadi

Publisher: John Wiley & Sons

Published: 2013-06-24

Total Pages: 204

ISBN-13: 1118034295

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Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.