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Author : Bendek B. Hansen
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.:/5 (34 download)
Download or read book Minimax Expected Length Confidence Intervals written by Bendek B. Hansen and published by . This book was released on 2000 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lorenz Biegler
Publisher : John Wiley & Sons
ISBN 13 : 1119957583
Total Pages : 403 pages
Book Rating : 4.1/5 (199 download)
Download or read book Large-Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by John Wiley & Sons. This book was released on 2011-06-24 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Author : Djalma Galvao Carneiro Pessoa
Publisher :
ISBN 13 :
Total Pages : 69 pages
Book Rating : 4.:/5 (219 download)
Download or read book Asymptotically Minimax Fixed Length Confidence Intervals written by Djalma Galvao Carneiro Pessoa and published by . This book was released on 1971 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Diane E. Duffy
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.E/5 ( download)
Download or read book Confidence Intervals for a Binomial Parameter Based on Multistage Tests written by Diane E. Duffy and published by . This book was released on 1986 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chad Michael Schafer
Publisher :
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.:/5 (34 download)
Download or read book Constructing Confidence Regions of Optimal Expected Size written by Chad Michael Schafer and published by . This book was released on 2004 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : F. C. Leone
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Use of Sample Quasi-ranges in Setting Confidence Intervals for the Population Standard Deviation written by F. C. Leone and published by . This book was released on 1960 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : MANOJ KUMAR SRIVASTAVA
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812034930X
Total Pages : 817 pages
Book Rating : 4.1/5 (23 download)
Download or read book STATISTICAL INFERENCE : THEORY OF ESTIMATION written by MANOJ KUMAR SRIVASTAVA and published by PHI Learning Pvt. Ltd.. This book was released on 2014-04-03 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.
Author : Jarrod Tuck
Publisher :
ISBN 13 :
Total Pages : 506 pages
Book Rating : 4.:/5 (431 download)
Download or read book Confidence Intervals Incorporating Prior Information written by Jarrod Tuck and published by . This book was released on 2006 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This theis proposes a new approach to constructing a 1 - DC confidence interval in a large sample regression setting. This new approach utilises compromise decision theory to incorporate prior information about the nuisance regression parameter so that when it is true, the interval length is shorter than the standard 1 - DC confidence interval. This appraoch produces an interval called the Confidence Interval Incorporating Prior Information. In addition, this theory provides a performance bound on any 1- DC confidence interval. Compromise decision theory is then applied to find a 1 - DC confidence interval for the difference of two population means, when there is uncertain prior information that the population variances are equal. Here we show that, in terms of confidence interval expected length, there does not exist a 1 - DC confidence interval that provides a significant improvement over the Welch confidence interval whose length has been adjusted so that its minimum coverage is 1 - DC.
Author : George G. Roussas
Publisher : Academic Press
ISBN 13 : 9780125993159
Total Pages : 602 pages
Book Rating : 4.9/5 (931 download)
Download or read book A Course in Mathematical Statistics written by George G. Roussas and published by Academic Press. This book was released on 1997-02-28 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference. * Contains 25% new material * Includes the most complete coverage of sufficiency * Transformation of Random Vectors * Sufficiency / Completeness / Exponential Families * Order Statistics * Elements of Nonparametric Density Estimation * Analysis of Variance (ANOVA) * Regression Analysis * Linear Models
Author : Constantinos Goutis
Publisher :
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.E/5 ( download)
Download or read book Improved Invariant Set Estimation of a Normal Variance with Generalizations written by Constantinos Goutis and published by . This book was released on 1989 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zijian Guo
Publisher :
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.:/5 (131 download)
Download or read book Statistical Inference for High-Dimensional Linear Models written by Zijian Guo and published by . This book was released on 2017 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional linear models play an important role in the analysis of modern data sets. Although the estimation problem has been well understood, there is still a paucity of methods and theories on the inference problem for high-dimensional linear models. This thesis focuses on statistical inference for high-dimensional linear models and consists of the following three parts. 1. The first part of the thesis considers confidence intervals for linear functionals in high-dimensional linear regression. We first establish the convergence rates of the minimax expected length for confidence intervals. Furthermore, we investigate the problem of adaptation to sparsity for the construction of confidence intervals and identify the regimes in which it is possible to construct adaptive confidence intervals. 2. In the second part of the thesis, we consider point and interval estimation of the lq loss of a given estimator in high-dimensional linear regression. For the class of rate-optimal estimators, we establish the minimax rates for estimating their lq losses, the minimax expected length of confidence intervals for their lq losses and the possibility of adaptivity of confidence intervals for their lq losses. 3. In the third part of the thesis, we consider the problem in the framework of high-dimensional instrumental variable regression and construct confidence intervals for the treatment effect in the presence of possibly invalid instrumental variables. We develop a novel selection procedure, Two-Stage Hard Thresholding (TSHT) to select valid instrumental variables and construct honest confidence intervals for the treatment effect using the selected instrumental variables.
Author : Jun Shao
Publisher : Springer Science & Business Media
ISBN 13 : 0387217185
Total Pages : 607 pages
Book Rating : 4.3/5 (872 download)
Download or read book Mathematical Statistics written by Jun Shao and published by Springer Science & Business Media. This book was released on 2008-02-03 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. This new edition has been revised and updated and in this fourth printing, errors have been ironed out. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Subsequent chapters contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.
Author :
Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.E/5 ( download)
Download or read book Applied Statistics in Agriculture written by and published by . This book was released on 2002 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Burdick
Publisher : CRC Press
ISBN 13 : 9780824786441
Total Pages : 238 pages
Book Rating : 4.7/5 (864 download)
Download or read book Confidence Intervals on Variance Components written by Burdick and published by CRC Press. This book was released on 1992-02-28 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summarizes information scattered in the technical literature on a subject too new to be included in most textbooks, but which is of interest to statisticians, and those who use statistics in science and education, at an advanced undergraduate or higher level. Overviews recent research on constructin
Author : Glenn Edward Norman Shorrock
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.:/5 (153 download)
Download or read book A Minimax Generalized Bayes Confidence Interval for a Normal Variance written by Glenn Edward Norman Shorrock and published by . This book was released on 1981 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yichuan Xia
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (129 download)
Download or read book Interval Estimation for the Difference of Two Binomial Proportions in Non-adaptive and Adaptive Designs written by Yichuan Xia and published by . This book was released on 2002 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Khageswor Giri
Publisher :
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4.:/5 (388 download)
Download or read book Confidence Intervals in Regression Utilizing Prior Information written by Khageswor Giri and published by . This book was released on 2008 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: We use the form of the naive 1 - DC[alpha] confidence interval to motivate a new frequentist 1 - DC[alpha] confidence interval that utilizes uncertain prior information about the regression parameters. This interval has expected length that (a) is relatively small when this prior information is correct and (b) has maximum value that is not too large. It has coverage probability 1 - DC[alpha] throughout the parameter space and, unlike the naive confidence interval, has endpoints that are continuous functions of the data. Additionally, this interval coincides with the standard 1 - DC[alpha] confidence interval when the data happens to strongly contradict the prior information. We then use compromise decision theory to find bounds on the performance of this new confidence interval for large samples. Finally, we consider a 2 x 2 factorial experiment with more than one replicate. We describe new simultaneous frequentist confidence intervals for the population cell means, with simultaneous confidence coefficient 1 - DC[alpha], that utilize uncertain prior information that the two-factor interaction is zero.
