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Semimartingales And Their Statistical Inference
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Book Synopsis Semimartingales and their Statistical Inference by : B.L.S. Prakasa Rao
Download or read book Semimartingales and their Statistical Inference written by B.L.S. Prakasa Rao and published by CRC Press. This book was released on 1999-05-11 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.
Book Synopsis Associated Sequences, Demimartingales and Nonparametric Inference by : B.L.S. Prakasa Rao
Download or read book Associated Sequences, Demimartingales and Nonparametric Inference written by B.L.S. Prakasa Rao and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.
Book Synopsis Statistical Inference Based on the likelihood by : Adelchi Azzalini
Download or read book Statistical Inference Based on the likelihood written by Adelchi Azzalini and published by Routledge. This book was released on 2017-11-13 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.
Book Synopsis Martingale Methods in Statistics by : Yoichi Nishiyama
Download or read book Martingale Methods in Statistics written by Yoichi Nishiyama and published by CRC Press. This book was released on 2021-11-24 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Methods in Statistics provides a unique introduction to statistics of stochastic processes written with the author’s strong desire to present what is not available in other textbooks. While the author chooses to omit the well-known proofs of some of fundamental theorems in martingale theory by making clear citations instead, the author does his best to describe some intuitive interpretations or concrete usages of such theorems. On the other hand, the exposition of relatively new theorems in asymptotic statistics is presented in a completely self-contained way. Some simple, easy-to-understand proofs of martingale central limit theorems are included. The potential readers include those who hope to build up mathematical bases to deal with high-frequency data in mathematical finance and those who hope to learn the theoretical background for Cox’s regression model in survival analysis. A highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics, such as the asymptotic representation of Z-estimators, the theory of asymptotically optimal inference based on the LAN concept and the unified approach to the change point problems via "Z-process method". Some new inequalities for maxima of finitely many martingales are presented in the Appendix. Readers will find many tips for solving concrete problems in modern statistics of stochastic processes as well as in more fundamental models such as i.i.d. and Markov chain models.
Book Synopsis Asymptotic Statistics by : Reinhard Höpfner
Download or read book Asymptotic Statistics written by Reinhard Höpfner and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-05-26 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes. The book can be read in different ways, according to possibly different mathematical preferences of the reader. One reader may focus on the statistical theory, and thus on the chapters about Gaussian shift models, mixed normal and quadratic models, and on local asymptotics where the limit model is a Gaussian shift or a mixed normal or a quadratic experiment (LAN, LAMN, LAQ). Another reader may prefer an introduction to stochastic process models where given statistical results apply, and thus concentrate on subsections or chapters on likelihood ratio processes and some diffusion type models where LAN, LAMN or LAQ occurs. Finally, readers might put together both aspects. The book is suitable for graduate students starting to work in statistics of stochastic processes, as well as for researchers interested in a precise introduction to this area.
Book Synopsis Local Polynomial Modelling and Its Applications by : Jianqing Fan
Download or read book Local Polynomial Modelling and Its Applications written by Jianqing Fan and published by Routledge. This book was released on 2018-05-02 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.
Book Synopsis Uncertainty And Optimality: Probability, Statistics And Operations Research by : Jagadis Chandra Misra
Download or read book Uncertainty And Optimality: Probability, Statistics And Operations Research written by Jagadis Chandra Misra and published by World Scientific. This book was released on 2002-11-05 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with different modern topics in probability, statistics and operations research. It has been written lucidly in a novel way. Wherever necessary, the theory is explained in great detail, with suitable illustrations. Numerous references are given, so that young researchers who want to start their work in a particular area will benefit immensely from the book.The contributors are distinguished statisticians and operations research experts from all over the world.
Book Synopsis Statistical Analysis of Spatial and Spatio-Temporal Point Patterns by : Peter J. Diggle
Download or read book Statistical Analysis of Spatial and Spatio-Temporal Point Patterns written by Peter J. Diggle and published by CRC Press. This book was released on 2013-07-23 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent statistician and author, the first edition of this bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of spatial point patterns. Retaining all the material from the second edition and adding substantial new material, Statistical Analysis of Spatial and Spatio-Temporal Point Patter
Book Synopsis Statistical Learning with Sparsity by : Trevor Hastie
Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Book Synopsis Measuring Statistical Evidence Using Relative Belief by : Michael Evans
Download or read book Measuring Statistical Evidence Using Relative Belief written by Michael Evans and published by CRC Press. This book was released on 2015-06-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It attempts to establish a gold standard for how a statistical analysis should proceed. The book illustrates relative belief theory using many examples and describes the strengths and weaknesses of the theory. The author also addresses fundamental statistical issues, including the meaning of probability, the role of subjectivity, the meaning of objectivity, and the role of infinity and continuity.
Book Synopsis Robust Nonparametric Statistical Methods by : Thomas P. Hettmansperger
Download or read book Robust Nonparametric Statistical Methods written by Thomas P. Hettmansperger and published by CRC Press. This book was released on 2010-12-20 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting an extensive set of tools and methods for data analysis, Robust Nonparametric Statistical Methods, Second Edition covers univariate tests and estimates with extensions to linear models, multivariate models, times series models, experimental designs, and mixed models. It follows the approach of the first edition by developing rank-based m
Book Synopsis Statistical Methods for Stochastic Differential Equations by : Mathieu Kessler
Download or read book Statistical Methods for Stochastic Differential Equations written by Mathieu Kessler and published by CRC Press. This book was released on 2012-05-17 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.
Book Synopsis Statistical Methods for Spatio-Temporal Systems by : Barbel Finkenstadt
Download or read book Statistical Methods for Spatio-Temporal Systems written by Barbel Finkenstadt and published by CRC Press. This book was released on 2006-10-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts w
Book Synopsis Statistical Portfolio Estimation by : Masanobu Taniguchi
Download or read book Statistical Portfolio Estimation written by Masanobu Taniguchi and published by CRC Press. This book was released on 2017-09-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered. This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.
Book Synopsis Introduction to High-Dimensional Statistics by : Christophe Giraud
Download or read book Introduction to High-Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2014-12-17 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever-greater computing technologies have given rise to an exponentially growing volume of data. Today massive data sets (with potentially thousands of variables) play an important role in almost every branch of modern human activity, including networks, finance, and genetics. However, analyzing such data has presented a challenge for statisticians
Book Synopsis Semialgebraic Statistics and Latent Tree Models by : Piotr Zwiernik
Download or read book Semialgebraic Statistics and Latent Tree Models written by Piotr Zwiernik and published by CRC Press. This book was released on 2015-08-21 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints
Book Synopsis Expansions and Asymptotics for Statistics by : Christopher G. Small
Download or read book Expansions and Asymptotics for Statistics written by Christopher G. Small and published by CRC Press. This book was released on 2010-05-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. The book first discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, and the study of rational approximations to functions. With a focus on asymptotic normality and asymptotic efficiency of standard estimators, it covers various applications, such as the use of the delta method for bias reduction, variance stabilisation, and the construction of normalising transformations, as well as the standard theory derived from the work of R.A. Fisher, H. Cramér, L. Le Cam, and others. The book then examines the close connection between saddle-point approximation and the Laplace method. The final chapter explores series convergence and the acceleration of that convergence.
