Essentials of Statistical Inference

Essentials of Statistical Inference

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  • Author: G. A. Young
  • Publisher: Cambridge University Press
  • ISBN: 9780521839716
  • Category : Mathematics
  • Languages : en
  • Pages : 240

Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, this engaging textbook gives a concise account of the main approaches to inference, with particular emphasis on the contrasts between them. It is the first textbook to synthesize contemporary material on computational topics with basic mathematical theory.


Fundamentals of Nonparametric Bayesian Inference

Fundamentals of Nonparametric Bayesian Inference

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  • Author: Subhashis Ghosal
  • Publisher: Cambridge University Press
  • ISBN: 0521878268
  • Category : Business & Economics
  • Languages : en
  • Pages : 671

Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.


Principles of Statistical Inference

Principles of Statistical Inference

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  • Author: D. R. Cox
  • Publisher: Cambridge University Press
  • ISBN: 1139459139
  • Category : Mathematics
  • Languages : en
  • Pages : 227

In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.


Elements of Distribution Theory

Elements of Distribution Theory

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  • Author: Thomas A. Severini
  • Publisher: Cambridge University Press
  • ISBN: 1139446118
  • Category : Mathematics
  • Languages : en
  • Pages : 3

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.


Confidence, Likelihood, Probability

Confidence, Likelihood, Probability

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  • Author: Tore Schweder
  • Publisher: Cambridge University Press
  • ISBN: 1316445054
  • Category : Mathematics
  • Languages : en
  • Pages : 521

This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors. This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman–Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.


High-Dimensional Statistics

High-Dimensional Statistics

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  • Author: Martin J. Wainwright
  • Publisher: Cambridge University Press
  • ISBN: 1108498027
  • Category : Business & Economics
  • Languages : en
  • Pages : 571

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.


Computer Age Statistical Inference

Computer Age Statistical Inference

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  • Author: Bradley Efron
  • Publisher: Cambridge University Press
  • ISBN: 1108107958
  • Category : Mathematics
  • Languages : en
  • Pages : 496

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.


Theoretical Statistics

Theoretical Statistics

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  • Author: Robert W. Keener
  • Publisher: Springer Science & Business Media
  • ISBN: 0387938397
  • Category : Mathematics
  • Languages : en
  • Pages : 543

Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.


Bayesian Nonparametrics

Bayesian Nonparametrics

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  • Author: J.K. Ghosh
  • Publisher: Springer Science & Business Media
  • ISBN: 0387226540
  • Category : Mathematics
  • Languages : en
  • Pages : 311

This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.


Mathematical Foundations of Infinite-Dimensional Statistical Models

Mathematical Foundations of Infinite-Dimensional Statistical Models

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  • Author: Evarist Giné
  • Publisher: Cambridge University Press
  • ISBN: 1009022784
  • Category : Mathematics
  • Languages : en
  • Pages : 706

In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.