U Statistics Mm Estimators And Resampling
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U Statistics Mm Estimators And Resampling
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Author : Arup Bose
language : en
Publisher: Springer
Release Date : 2018-08-28
U Statistics Mm Estimators And Resampling written by Arup Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.
Random Circulant Matrices
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2018-11-05
Random Circulant Matrices written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Random Matrices And Non Commutative Probability
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Author : Arup Bose
language : en
Publisher: CRC Press
Release Date : 2021-10-26
Random Matrices And Non Commutative Probability written by Arup Bose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-26 with Mathematics categories.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Measure And Integration
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Author : S. Kesavan
language : en
Publisher: Springer
Release Date : 2019-02-25
Measure And Integration written by S. Kesavan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-25 with Mathematics categories.
This book deals with topics on the theory of measure and integration. It starts with discussion on the Riemann integral and points out certain shortcomings, which motivate the theory of measure and the Lebesgue integral. Most of the material in this book can be covered in a one-semester introductory course. An awareness of basic real analysis and elementary topological notions, with special emphasis on the topology of the n-dimensional Euclidean space, is the pre-requisite for this book. Each chapter is provided with a variety of exercises for the students. The book is targeted to students of graduate- and advanced-graduate-level courses on the theory of measure and integration.
Statistical Data Analysis Based On The L1 Norm And Related Methods
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Author : Yadolah Dodge
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Statistical Data Analysis Based On The L1 Norm And Related Methods written by Yadolah Dodge and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains a selection of invited papers, presented to the fourth In Statistical Analysis Based on the L1-Norm and Related ternational Conference on Methods, held in Neuchatel, Switzerland, from August 4-9, 2002. Organized jointly by the University of Illinois at Chicago (Gib Bassett), the Rutgers University (Regina Liu and Yehuda Vardi) and the University of Neuchatel (Yadolah Dodge), the conference brought together experts whose research deals with theory and ap plications involving the L1-Norm. The conference included invited and contributed talks as well as a tutorial on Quantile Regression. This volume includes 36 refereed invited papers under seven headings. Part one deals with Quantiles in all their forms and shapes. It includes papers on quantile functions in non-parametric multivariate analysis, and empirical applications of quantile regression. Much of the development in this direction follows from the fundamental paper by Koenker and Bassett in 1978. Financial and Time Series A nalysis follows the section on quantiles. Part three concerns Estimation, Testing and Characterization. Part four, Deep in the Data, deals with issues related to data depth. Part five addresses Classification questions. The problem of Density Estimation and Image Processing is discussed in Part six, and finally Part seven presents two environmental applications. The contributions represent clear evidence of important research involving theo retical issues and applications associated with the L1-Norm. It is my hope that the articles contained in this volume and its predecessors, published in 1987, 1992, and 1997, will stimulate interest among researchers.
Encyclopedia Of Statistical Sciences Volume 12
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Author :
language : en
Publisher: John Wiley & Sons
Release Date : 2005-12-16
Encyclopedia Of Statistical Sciences Volume 12 written by and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-16 with Mathematics categories.
ENCYCLOPEDIA OF STATISTICAL SCIENCES
Journal Of Statistical Planning And Inference
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Author :
language : en
Publisher:
Release Date : 2003
Journal Of Statistical Planning And Inference written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Electronic journals categories.
Recent Advances And Trends In Nonparametric Statistics
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Author : M.G. Akritas
language : en
Publisher: Elsevier
Release Date : 2003-10-31
Recent Advances And Trends In Nonparametric Statistics written by M.G. Akritas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-31 with Mathematics categories.
The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.Key features:• algorithic approaches • wavelets and nonlinear smoothers • graphical methods and data mining • biostatistics and bioinformatics • bagging and boosting • support vector machines • resampling methods
Handbook Of Econometrics
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Author : J.J. Heckman
language : en
Publisher: Elsevier
Release Date : 2001-11-22
Handbook Of Econometrics written by J.J. Heckman and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-22 with Business & Economics categories.
The Handbook is a definitive reference source and teaching aid for econometricians. It examines models, estimation theory, data analysis and field applications in econometrics. Comprehensive surveys, written by experts, discuss recent developments at a level suitable for professional use by economists, econometricians, statisticians, and in advanced graduate econometrics courses. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes
Essential Statistical Inference
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Author : Dennis D. Boos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-06
Essential Statistical Inference written by Dennis D. Boos 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 2013-02-06 with Mathematics categories.
This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods.