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Author: STANFORD UNIV CA DEPT OF STATISTICS.
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Generalized additive models extended the class of generalized linear models by allowing an arbitrary smooth function for any or all of the covariates. The functions are established by the local scoring procedure, using a smoother as a building block in an iterative algorithm. This paper utilizes a cubic spline smoother in the algorithm and show how the resultant procedure can be view as a method for automatically smoothing a suitably defined partial residual, and more formally, a method for maximizing a penalized likelihood. The authors also examine convergence of the inner (backfitting) loop in this case and illustrate these ideas with some binary response data. Keywords: Spline; Non-parametric regression.
Author: STANFORD UNIV CA DEPT OF STATISTICS.
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Get Book Here
Book Description
Generalized additive models extended the class of generalized linear models by allowing an arbitrary smooth function for any or all of the covariates. The functions are established by the local scoring procedure, using a smoother as a building block in an iterative algorithm. This paper utilizes a cubic spline smoother in the algorithm and show how the resultant procedure can be view as a method for automatically smoothing a suitably defined partial residual, and more formally, a method for maximizing a penalized likelihood. The authors also examine convergence of the inner (backfitting) loop in this case and illustrate these ideas with some binary response data. Keywords: Spline; Non-parametric regression.
Author: Simon Wood
Publisher: CRC Press
ISBN: 1584884746
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.
Author: T.J. Hastie
Publisher: Routledge
ISBN: 1351445960
Category : Mathematics
Languages : en
Pages : 356
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Book Description
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.
Author: P.J. Green
Publisher: CRC Press
ISBN: 9780412300400
Category : Mathematics
Languages : en
Pages : 198
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Book Description
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.
Author: Daowen Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 342
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Book Description
Author: Trevor Hastie
Publisher:
ISBN:
Category : Random walks (Mathematics)
Languages : en
Pages : 19
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Book Description
Author: Havard Rue
Publisher: CRC Press
ISBN: 0203492021
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie
Author: Mikis D. Stasinopoulos
Publisher: CRC Press
ISBN: 1351980378
Category : Mathematics
Languages : en
Pages : 641
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Book Description
This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.
Author: Jonathon D. Brown
Publisher: Springer
ISBN: 3319935496
Category : Social Science
Languages : en
Pages : 526
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Book Description
This book demonstrates the importance of computer-generated statistical analyses in behavioral science research, particularly those using the R software environment. Statistical methods are being increasingly developed and refined by computer scientists, with expertise in writing efficient and elegant computer code. Unfortunately, many researchers lack this programming background, leaving them to accept on faith the black-box output that emerges from the sophisticated statistical models they frequently use. Building on the author’s previous volume, Linear Models in Matrix Form, this text bridges the gap between computer science and research application, providing easy-to-follow computer code for many statistical analyses using the R software environment. The text opens with a foundational section on linear algebra, then covers a variety of advanced topics, including robust regression, model selection based on bias and efficiency, nonlinear models and optimization routines, generalized linear models, and survival and time-series analysis. Each section concludes with a presentation of the computer code used to illuminate the analysis, as well as pointers to packages in R that can be used for similar analyses and nonstandard cases. The accessible code and breadth of topics make this book an ideal tool for graduate students or researchers in the behavioral sciences who are interested in performing advanced statistical analyses without having a sophisticated background in computer science and mathematics.
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
ISBN: 3642484255
Category : Business & Economics
Languages : en
Pages : 265
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Book Description
One of the main applications of statistical smoothing techniques is nonparametric regression. For the last 15 years there has been a strong theoretical interest in the development of such techniques. Related algorithmic concepts have been a main concern in computational statistics. Smoothing techniques in regression as well as other statistical methods are increasingly applied in biosciences and economics. But they are also relevant for medical and psychological research. Introduced are new developments in scatterplot smoothing and applications in statistical modelling. The treatment of the topics is on an intermediate level avoiding too much technicalities. Computational and applied aspects are considered throughout. Of particular interest to readers is the discussion of recent local fitting techniques.
