Nonparametric Regression and Generalized Linear Models

A roughness penalty approach

Author: P.J. Green,Bernard. W. Silverman

Publisher: CRC Press

ISBN: 9780412300400

Category: Mathematics

Page: 184

View: 8832

In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts. The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus. This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.
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Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 9780203492284

Category: Mathematics

Page: 312

View: 5564

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at http://people.bath.ac.uk/jjf23/ELM/ Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.
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Regression

Modelle, Methoden und Anwendungen

Author: Ludwig Fahrmeir,Thomas Kneib,Stefan Lang

Publisher: Springer-Verlag

ISBN: 3642018378

Category: Business & Economics

Page: 502

View: 499

In dem Band beschreiben die Autoren erstmals klassische Regressionsansätze und moderne nicht- und semiparametrische Methoden in einer integrierten und anwendungsorientierten Form. Um Lesern die Analyse eigener Fragestellungen zu ermöglichen, demonstrieren sie die praktische Anwendung der Konzepte und Methoden anhand ausführlicher Fallstudien. Geeignet für Studierende der Statistik sowie für Wissenschaftler und Praktiker, zum Beispiel in den Wirtschafts- und Sozialwissenschaften, der Bioinformatik und -statistik, Ökonometrie und Epidemiologie.
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Multiple and Generalized Nonparametric Regression

Author: John Fox

Publisher: SAGE Publications

ISBN: 1544332602

Category: Social Science

Page: 96

View: 5929

This book builds on John Fox's previous volume in the QASS Series, Non Parametric Simple Regression. In this book, the reader learns how to estimate and plot smooth functions when there are multiple independent variables.
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Nonparametric Regression and Spline Smoothing, Second Edition

Author: Randall L. Eubank

Publisher: CRC Press

ISBN: 9780824793371

Category: Mathematics

Page: 360

View: 8381

Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.
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Applied Regression Analysis and Generalized Linear Models

Author: John Fox

Publisher: SAGE Publications

ISBN: 1483321312

Category: Social Science

Page: 816

View: 1289

Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book.
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Introduction to Nonparametric Regression

Author: K. Takezawa

Publisher: John Wiley & Sons

ISBN: 0471771449

Category: Mathematics

Page: 640

View: 1181

An easy-to-grasp introduction to nonparametric regression This book's straightforward, step-by-step approach provides anexcellent introduction to the field for novices of nonparametricregression. Introduction to Nonparametric Regression clearlyexplains the basic concepts underlying nonparametric regression andfeatures: * Thorough explanations of various techniques, which avoid complexmathematics and excessive abstract theory to help readersintuitively grasp the value of nonparametric regressionmethods * Statistical techniques accompanied by clear numerical examplesthat further assist readers in developing and implementing theirown solutions * Mathematical equations that are accompanied by a clearexplanation of how the equation was derived The first chapter leads with a compelling argument for studyingnonparametric regression and sets the stage for more advanceddiscussions. In addition to covering standard topics, such askernel and spline methods, the book provides in-depth coverage ofthe smoothing of histograms, a topic generally not covered incomparable texts. With a learning-by-doing approach, each topical chapter includesthorough S-Plus? examples that allow readers to duplicate the sameresults described in the chapter. A separate appendix is devoted tothe conversion of S-Plus objects to R objects. In addition, eachchapter ends with a set of problems that test readers' grasp of keyconcepts and techniques and also prepares them for more advancedtopics. This book is recommended as a textbook for undergraduate andgraduate courses in nonparametric regression. Only a basicknowledge of linear algebra and statistics is required. Inaddition, this is an excellent resource for researchers andengineers in such fields as pattern recognition, speechunderstanding, and data mining. Practitioners who rely onnonparametric regression for analyzing data in the physical,biological, and social sciences, as well as in finance andeconomics, will find this an unparalleled resource.
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Predictive Modeling Applications in Actuarial Science: Volume 1, Predictive Modeling Techniques

Author: Edward W. Frees,Richard A. Derrig,Glenn Meyers

Publisher: Cambridge University Press

ISBN: 1139992317

Category: Business & Economics

Page: N.A

View: 2452

Predictive modeling involves the use of data to forecast future events. It relies on capturing relationships between explanatory variables and the predicted variables from past occurrences and exploiting this to predict future outcomes. Forecasting future financial events is a core actuarial skill - actuaries routinely apply predictive-modeling techniques in insurance and other risk-management applications. This book is for actuaries and other financial analysts who are developing their expertise in statistics and wish to become familiar with concrete examples of predictive modeling. The book also addresses the needs of more seasoned practising analysts who would like an overview of advanced statistical topics that are particularly relevant in actuarial practice. Predictive Modeling Applications in Actuarial Science emphasizes lifelong learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used by analysts to gain a competitive advantage in situations with complex data.
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Predictive Modeling Applications in Actuarial Science

Author: Edward W. Frees,Richard A. Derrig,Glenn Meyers

Publisher: Cambridge University Press

ISBN: 1107029872

Category: Business & Economics

Page: 544

View: 7512

This book is for actuaries and financial analysts developing their expertise in statistics and who wish to become familiar with concrete examples of predictive modeling.
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Semimartingales and their Statistical Inference

Author: B.L.S. Prakasa Rao

Publisher: CRC Press

ISBN: 9781584880080

Category: Mathematics

Page: 450

View: 4560

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.
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Multivariate Statistical Modelling Based on Generalized Linear Models

Author: Ludwig Fahrmeir,Gerhard Tutz

Publisher: Springer Science & Business Media

ISBN: 1489900101

Category: Mathematics

Page: 426

View: 3614

Concerned with the use of generalised linear models for univariate and multivariate regression analysis, this is a detailed introductory survey of the subject, based on the analysis of real data drawn from a variety of subjects such as the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account.
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Modern Methods for Robust Regression

Author: Robert Andersen

Publisher: SAGE

ISBN: 1412940729

Category: Social Science

Page: 107

View: 1566

Geared towards both future and practising social scientists, this book takes an applied approach and offers readers empirical examples to illustrate key concepts. It includes: applied coverage of a topic that has traditionally been discussed from a theoretical standpoint; empirical examples to illustrate key concepts; a web appendix that provides readers with the data and the R-code for the examples used in the book.
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Generalized Additive Models

Author: T.J. Hastie

Publisher: Routledge

ISBN: 1351445960

Category: Mathematics

Page: 352

View: 8836

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.
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Smoothing and Regression

Approaches, Computation, and Application

Author: Michael G. Schimek

Publisher: John Wiley & Sons

ISBN: 1118763300

Category: Mathematics

Page: 640

View: 6731

A comprehensive introduction to a wide variety of univariate andmultivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Applicationbridges the many gaps that exist among competing univariate andmultivariate smoothing techniques. It introduces, describes, and insome cases compares a large number of the latest and most advancedtechniques for regression modeling. Unlike many other volumes onthis topic, which are highly technical and specialized, this bookdiscusses all methods in light of both computational efficiency andtheir applicability for real data analysis. Using examples of applications from the biosciences, environmentalsciences, engineering, and economics, as well as medical researchand marketing, this volume addresses the theory, computation, andapplication of each approach. A number of the techniques discussed,such as smoothing under shape restrictions or of dependent data,are presented for the first time in book form. Special features ofthis book include: * Comprehensive coverage of smoothing and regression with softwarehints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from aroundthe world * More than 150 illustrations also covering new graphicaltechniques important for exploratory data analysis andvisualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, appliedmathematics, computer science, and econometrics, as well as forresearchers in the applied and social sciences, Smoothing andRegression is a unique and important new resource destined tobecome one the most frequently consulted references in the field.
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Data Mining Algorithms

Explained Using R

Author: Pawel Cichosz

Publisher: John Wiley & Sons

ISBN: 1118950801

Category: Mathematics

Page: 720

View: 2203

Data Mining Algorithms is a practical, technically-oriented guide to data mining algorithms that covers the most important algorithms for building classification, regression, and clustering models, as well as techniques used for attribute selection and transformation, model quality evaluation, and creating model ensembles. The author presents many of the important topics and methodologies widely used in data mining, whilst demonstrating the internal operation and usage of data mining algorithms using examples in R.
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Data Analysis and Data Mining

An Introduction

Author: Adelchi Azzalini,Bruno Scarpa

Publisher: Oxford University Press

ISBN: 0199942714

Category: Business & Economics

Page: 288

View: 3221

An introduction to statistical data mining, Data Analysis and Data Mining is both textbook and professional resource. Assuming only a basic knowledge of statistical reasoning, it presents core concepts in data mining and exploratory statistical models to students and professional statisticians-both those working in communications and those working in a technological or scientific capacity-who have a limited knowledge of data mining. This book presents key statistical concepts by way of case studies, giving readers the benefit of learning from real problems and real data. Aided by a diverse range of statistical methods and techniques, readers will move from simple problems to complex problems. Through these case studies, authors Adelchi Azzalini and Bruno Scarpa explain exactly how statistical methods work; rather than relying on the "push the button" philosophy, they demonstrate how to use statistical tools to find the best solution to any given problem. Case studies feature current topics highly relevant to data mining, such web page traffic; the segmentation of customers; selection of customers for direct mail commercial campaigns; fraud detection; and measurements of customer satisfaction. Appropriate for both advanced undergraduate and graduate students, this much-needed book will fill a gap between higher level books, which emphasize technical explanations, and lower level books, which assume no prior knowledge and do not explain the methodology behind the statistical operations.
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Extreme Value Methods with Applications to Finance

Author: Serguei Y. Novak

Publisher: CRC Press

ISBN: 1439835748

Category: Mathematics

Page: 399

View: 4536

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
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Fast Compact Algorithms and Software for Spline Smoothing

Author: Howard L. Weinert

Publisher: Springer Science & Business Media

ISBN: 1461454964

Category: Computers

Page: 45

View: 4804

Fast Compact Algorithms and Software for Spline Smoothing investigates algorithmic alternatives for computing cubic smoothing splines when the amount of smoothing is determined automatically by minimizing the generalized cross-validation score. These algorithms are based on Cholesky factorization, QR factorization, or the fast Fourier transform. All algorithms are implemented in MATLAB and are compared based on speed, memory use, and accuracy. An overall best algorithm is identified, which allows very large data sets to be processed quickly on a personal computer.
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