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Author : Ulhas Jayram Dixit
ISBN : 9789811008894
Genre : Mathematics
File Size : 26.21 MB
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This book discusses examples in parametric inference with R. Combining basic theory with modern approaches, it presents the latest developments and trends in statistical inference for students who do not have an advanced mathematical and statistical background. The topics discussed in the book are fundamental and common to many fields of statistical inference and thus serve as a point of departure for in-depth study. The book is divided into eight chapters: Chapter 1 provides an overview of topics on sufficiency and completeness, while Chapter 2 briefly discusses unbiased estimation. Chapter 3 focuses on the study of moments and maximum likelihood estimators, and Chapter 4 presents bounds for the variance. In Chapter 5, topics on consistent estimator are discussed. Chapter 6 discusses Bayes, while Chapter 7 studies some more powerful tests. Lastly, Chapter 8 examines unbiased and other tests. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability, will greatly benefit from this book. Students are expected to know matrix algebra, calculus, probability and distribution theory before beginning this course. Presenting a wealth of relevant solved and unsolved problems, the book offers an excellent tool for teachers and instructors who can assign homework problems from the exercises, and students will find the solved examples hugely beneficial in solving the exercise problems.

Author : Larry Wasserman
ISBN : 0387402721
Genre : Computers
File Size : 21.27 MB
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This book surveys a broad range of topics in probability and mathematical statistics. It provides the statistical background that a computer scientist needs to work in the area of machine learning.

Author : Jeffrey S. Racine
ISBN : 9780190900663
Genre : Business & Economics
File Size : 25.77 MB
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Linear time series methods -- Introduction to linear time series models -- Random walks, unit roots, and spurious relationships -- Univariate linear time series models -- Robust parametric inference -- Robust parametric estimation -- Model uncertainty -- Advance -- Bibliography -- Author index -- Subject index

Author : Michael R. Kosorok
ISBN : 0387749780
Genre : Mathematics
File Size : 66.15 MB
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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Author : Jesper Moller
ISBN : 0203496930
Genre : Mathematics
File Size : 36.92 MB
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Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Author : Alexandre Brouste
ISBN : 9780081012611
Genre : Business & Economics
File Size : 61.51 MB
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Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consisting of probability measures of an exponential type. However, the aforementioned applications also offer non-classical experiments implying observation samples of independent but not identically distributed random variables or even dependent random variables. Three examples of such experiments are treated in this book. First, the Generalized Linear Models are studied. They extend the standard regression model to non-Gaussian distributions. Statistical experiments with Markov chains are considered next. Finally, various statistical experiments generated by fractional Gaussian noise are also described. In this book, asymptotic properties of several sequences of estimators are detailed. The notion of asymptotical efficiency is discussed for the different statistical experiments considered in order to give the proper sense of estimation risk. Eighty examples and computations with R software are given throughout the text. Examines a range of statistical inference methods in the context of finance and insurance applications Presents the LAN (local asymptotic normality) property of likelihoods Combines the proofs of LAN property for different statistical experiments that appears in financial and insurance mathematics Provides the proper description of such statistical experiments and invites readers to seek optimal estimators (performed in R) for such statistical experiments

Author : John Kloke
ISBN : 9781439873441
Genre : Mathematics
File Size : 41.14 MB
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A Practical Guide to Implementing Nonparametric and Rank-Based Procedures Nonparametric Statistical Methods Using R covers traditional nonparametric methods and rank-based analyses, including estimation and inference for models ranging from simple location models to general linear and nonlinear models for uncorrelated and correlated responses. The authors emphasize applications and statistical computation. They illustrate the methods with many real and simulated data examples using R, including the packages Rfit and npsm. The book first gives an overview of the R language and basic statistical concepts before discussing nonparametrics. It presents rank-based methods for one- and two-sample problems, procedures for regression models, computation for general fixed-effects ANOVA and ANCOVA models, and time-to-event analyses. The last two chapters cover more advanced material, including high breakdown fits for general regression models and rank-based inference for cluster correlated data. The book can be used as a primary text or supplement in a course on applied nonparametric or robust procedures and as a reference for researchers who need to implement nonparametric and rank-based methods in practice. Through numerous examples, it shows readers how to apply these methods using R.

Author : Jong-Hyeon Jeong
ISBN : 9781493900053
Genre : Medical
File Size : 82.11 MB
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This is a monograph on the concept of residual life, which is an alternative summary measure of time-to-event data, or survival data. The mean residual life has been used for many years under the name of life expectancy, so it is a natural concept for summarizing survival or reliability data. It is also more interpretable than the popular hazard function, especially for communications between patients and physicians regarding the efficacy of a new drug in the medical field. This book reviews existing statistical methods to infer the residual life distribution. The review and comparison includes existing inference methods for mean and median, or quantile, residual life analysis through medical data examples. The concept of the residual life is also extended to competing risks analysis. The targeted audience includes biostatisticians, graduate students, and PhD (bio)statisticians. Knowledge in survival analysis at an introductory graduate level is advisable prior to reading this book.

Author : Ricardo A. Maronna
ISBN : 9781119214687
Genre : Mathematics
File Size : 74.55 MB
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A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Author : Jeffrey D. Long
ISBN : 9781412982689
Genre : Social Science
File Size : 48.89 MB
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This book is unique in its focus on showing students in the behavioral sciences how to analyze longitudinal data using R software. The book focuses on application, making it practical and accessible to students in psychology, education, and related fields, who have a basic foundation in statistics. It provides explicit instructions in R computer programming throughout the book, showing students exactly how a specific analysis is carried out and how output is interpreted.

Author : Christopher Clapham
ISBN : 9780191579769
Genre : Mathematics
File Size : 32.53 MB
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Authoritative and reliable, this A-Z provides jargon-free definitions for even the most technical mathematical terms. With 3,000 entries ranging from Achilles paradox to zero matrix, it covers all commonly encountered terms and concepts from pure and applied mathematics and statistics, for example, linear algebra, optimisation, nonlinear equations, and differential equations. In addition, there are entries on major mathematicians and on topics of more general interest, such as fractals, game theory, and chaos. Using graphs, diagrams, and charts to render definitions as comprehensible as possible, entries are clear and accessible and offer an ideal introduction to the subject. Useful appendices follow the A-Z dictionary and include lists of Nobel Prize winners and Fields' medallists, Greek letters, formulae, and - new to this edition - tables of inequalities, moments of inertia, Roman numerals, and more. This edition contains recommended web links at entry level, which are accessible and kept up to date via the Dictionary of Mathematics companion website. Fully revised and updated in line with curriculum and degree requirements this dictionary is indispensable for students and teachers of mathematics, and for anyone encountering mathematics in the workplace.

Author : Peter Müller
ISBN : 9783319189680
Genre : Mathematics
File Size : 48.61 MB
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This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.

Author : Larry Wasserman
ISBN : 0387306234
Genre : Mathematics
File Size : 42.82 MB
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This text provides the reader with a single book where they can find accounts of a number of up-to-date issues in nonparametric inference. The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book’s dual approach includes a mixture of methodology and theory.

Author : Maria L. Rizzo
ISBN : 9781584885450
Genre : Mathematics
File Size : 25.52 MB
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Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditional core material of computational statistics, with an emphasis on using the R language via an examples-based approach. Suitable for an introductory course in computational statistics or for self-study, it includes R code for all examples and R notes to help explain the R programming concepts. After an overview of computational statistics and an introduction to the R computing environment, the book reviews some basic concepts in probability and classical statistical inference. Each subsequent chapter explores a specific topic in computational statistics. These chapters cover the simulation of random variables from probability distributions, the visualization of multivariate data, Monte Carlo integration and variance reduction methods, Monte Carlo methods in inference, bootstrap and jackknife, permutation tests, Markov chain Monte Carlo (MCMC) methods, and density estimation. The final chapter presents a selection of examples that illustrate the application of numerical methods using R functions. Focusing on implementation rather than theory, this text serves as a balanced, accessible introduction to computational statistics and statistical computing.

Author : Luigi Pace
ISBN : 9812386947
Genre : Mathematics
File Size : 24.85 MB
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In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.

A treatment of the problems of inference associated with experiments in science, with the emphasis on techniques for dividing the sample information into various parts, such that the diverse problems of inference that arise from repeatable experiments may be addressed. A particularly valuable feature is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book evolved from the authors own courses on statistical inference, and assumes an introductory course in probability, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. While this is a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students, it may also be used as a reference book.

Author : Seymour Geisser
ISBN : 0412034719
Genre : Mathematics
File Size : 29.85 MB
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The author's research has been directed towards inference involving observables rather than parameters. In this book, he brings together his views on predictive or observable inference and its advantages over parametric inference. While the book discusses a variety of approaches to prediction including those based on parametric, nonparametric, and nonstochastic statistical models, it is devoted mainly to predictive applications of the Bayesian approach. It not only substitutes predictive analyses for parametric analyses, but it also presents predictive analyses that have no real parametric analogues. It demonstrates that predictive inference can be a critical component of even strict parametric inference when dealing with interim analyses. This approach to predictive inference will be of interest to statisticians, psychologists, econometricians, and sociologists.

Author : Christopher Z. Mooney
ISBN : 0803959435
Genre : Education
File Size : 87.19 MB
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The author explains the logic behind the method and demonstrates its uses for social and behavioral research in: conducting inference using statistics with only weak mathematical theory; testing null hypotheses under a variety of plausible conditions; assessing the robustness of parametric inference to violations of its assumptions; assessing the quality of inferential methods; and comparing the properties of two or more estimators. In addition, Christopher Z Mooney carefully demonstrates how to prepare computer algorithms using GAUSS code and uses several research examples to demonstrate these principles. This volume will enable researchers to execute Monte Carlo Simulation effectively and to interpret the estimated sampling distribution generated from its use.