Approximation Theorems of Mathematical Statistics
Author: R. J. Serfling
Publisher:
Published: 1980
Total Pages: 371
ISBN-13: 9780471137306
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Approximation Theorems of Mathematical Statistics
Author: Robert J. Serfling
Publisher: Wiley-Interscience
Published: 1980-12-08
Total Pages: 392
ISBN-13: 9780471024033
DOWNLOAD EBOOK →Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures
Approximation Theorems of Mathematical Statistics
Author: Robert J. Serfling
Publisher: John Wiley & Sons
Published: 2009-09-25
Total Pages: 392
ISBN-13: 0470317191
DOWNLOAD EBOOK →Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures
Modern concepts and theorems of mathematical statistics
Author: Edward B. Manoukian
Publisher: Springer Verlag
Published: 1986
Total Pages: 156
ISBN-13:
DOWNLOAD EBOOK →Mathematical Statistics and Limit Theorems
Author: Marc Hallin
Publisher: Springer
Published: 2016-10-05
Total Pages: 0
ISBN-13: 9783319353944
DOWNLOAD EBOOK →This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.
Strong Approximations in Probability and Statistics
Author: M. Csörgo
Publisher: Academic Press
Published: 2014-07-10
Total Pages: 287
ISBN-13: 1483268047
DOWNLOAD EBOOK →Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students.
Mathematical Statistics
Author: Aleksandr Petrovich Korostelev
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 258
ISBN-13: 0821852833
DOWNLOAD EBOOK →iPositive Give a man a fish, he eats for a day, but if you teach him to fish, you feed him for life. Such is the approach of iPositive. One day at the gym doesnt make a person fit for life; its a consistent dedication to getting the body in shape that eventually yields results. The lessons in iPositive work in much the same way: They challenge the reader to work to keep the mind in shape. The book is a powerful guide to personal happiness through positivity. Its concepts provide empowerment to overcome self-doubt, disbelief and inferiority complexes in order to transcend the negativity in life. iPositive is geared toward helping individuals become more focused on the things they most want in life, like happiness, love and success, or banish anchors that may be weighting them down, like stress, smoking or excess weight. The book gives readers the practical means to become more focused on those things they want in life, and serves as an inspirational manual for a life of fulfillment, and strength in body, mind and spirit.
Modern Concepts and Theorems of Mathematical Statistics
Author: Edward B. Manoukian
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 168
ISBN-13: 1461248566
DOWNLOAD EBOOK →With the rapid progress and development of mathematical statistical methods, it is becoming more and more important for the student, the in structor, and the researcher in this field to have at their disposal a quick, comprehensive, and compact reference source on a very wide range of the field of modern mathematical statistics. This book is an attempt to fulfill this need and is encyclopedic in nature. It is a useful reference for almost every learner involved with mathematical statistics at any level, and may supple ment any textbook on the subject. As the primary audience of this book, we have in mind the beginning busy graduate student who finds it difficult to master basic modern concepts by an examination of a limited number of existing textbooks. To make the book more accessible to a wide range of readers I have kept the mathematical language at a level suitable for those who have had only an introductory undergraduate course on probability and statistics, and basic courses in calculus and linear algebra. No sacrifice, how ever, is made to dispense with rigor. In stating theorems I have not always done so under the weakest possible conditions. This allows the reader to readily verify if such conditions are indeed satisfied in most applications given in modern graduate courses without being lost in extra unnecessary mathematical intricacies. The book is not a mere dictionary of mathematical statistical terms.
Approximate Computation of Expectations
Author: Charles Stein
Publisher: IMS
Published: 1986
Total Pages: 172
ISBN-13: 9780940600089
DOWNLOAD EBOOK →Theory of U-Statistics
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 558
ISBN-13: 9401735158
DOWNLOAD EBOOK →The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
