Semimartingales And Their Statistical Inference
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Semimartingales And Their Statistical Inference
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Author : B.L.S. Prakasa Rao
language : en
Publisher: CRC Press
Release Date : 1999-05-11
Semimartingales And Their Statistical Inference written by B.L.S. Prakasa Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-11 with Mathematics categories.
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.
Associated Sequences Demimartingales And Nonparametric Inference
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Author : B.L.S. Prakasa Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-04
Associated Sequences Demimartingales And Nonparametric Inference written by B.L.S. Prakasa Rao 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 2011-11-04 with Mathematics categories.
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.
Martingale Methods In Statistics
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Author : Yoichi Nishiyama
language : en
Publisher: CRC Press
Release Date : 2021-11-24
Martingale Methods In Statistics written by Yoichi Nishiyama and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-24 with Mathematics categories.
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.
Some Basic Theory For Statistical Inference
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Author : E.J.G. Pitman
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Some Basic Theory For Statistical Inference written by E.J.G. Pitman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
In this book the author presents with elegance and precision some of the basic mathematical theory required for statistical inference at a level which will make it readable by most students of statistics.
The Theory And Applications Of Statistical Interference Functions
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Author : D.L. McLeish
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Theory And Applications Of Statistical Interference Functions written by D.L. McLeish 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 monograph arose out of a desire to develop an approach to statistical infer ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.
Statistical Inference Based On Divergence Measures
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Author : Leandro Pardo
language : en
Publisher: CRC Press
Release Date : 2018-11-12
Statistical Inference Based On Divergence Measures written by Leandro Pardo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-12 with Mathematics categories.
The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this p
Statistical Inference
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Author : Ayanendranath Basu
language : en
Publisher: CRC Press
Release Date : 2011-06-22
Statistical Inference written by Ayanendranath Basu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-22 with Computers categories.
In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Stati
Statistical Inference
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Author : Murray Aitkin
language : en
Publisher: CRC Press
Release Date : 2010-06-02
Statistical Inference written by Murray Aitkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-02 with Mathematics categories.
Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct
Statistical Inference Based On The Likelihood
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Author : Adelchi Azzalini
language : en
Publisher: Routledge
Release Date : 2017-11-13
Statistical Inference Based On The Likelihood written by Adelchi Azzalini and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-13 with Mathematics categories.
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.
Simultaneous Statistical Inference
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Author : Rupert G. Jr. Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Simultaneous Statistical Inference written by Rupert G. Jr. Miller 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.
Simultaneous Statistical Inference, which was published originally in 1966 by McGraw-Hill Book Company, went out of print in 1973. Since then, it has been available from University Microfilms International in xerox form. With this new edition Springer-Verlag has republished the original edition along with my review article on multiple comparisons from the December 1977 issue of the Journal of the American Statistical Association. This review article covered developments in the field from 1966 through 1976. A few minor typographical errors in the original edition have been corrected in this new edition. A new table of critical points for the studentized maximum modulus is included in this second edition as an addendum. The original edition included the table by K. C. S. Pillai and K. V. Ramachandran, which was meager but the best available at the time. This edition contains the table published in Biometrika in 1971 by G. 1. Hahn and R. W. Hendrickson, which is far more comprehensive and therefore more useful. The typing was ably handled by Wanda Edminster for the review article and Karola Decleve for the changes for the second edition. My wife, Barbara, again cheerfully assisted in the proofreading. Fred Leone kindly granted permission from the American Statistical Association to reproduce my review article. Also, Gerald Hahn, Richard Hendrickson, and, for Biometrika, David Cox graciously granted permission to reproduce the new table of the studentized maximum modulus. The work in preparing the review article was partially supported by NIH Grant ROI GM21215.