Download or read book Smoothing Spline ANOVA Models and Their Applications in Complex and Massive Datasets written by Jingyi Zhang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex and massive datasets can be easily accessed using the newly developed data acquisition technology. In spite of the fact that the smoothing spline ANOVA models have proven to be useful in a variety of fields, these datasets impose the challenges on the applications of the models. In this chapter, we present a selected review of the smoothing spline ANOVA models and highlight some challenges and opportunities in massive datasets. We review two approaches to significantly reduce the computational costs of fitting the model. One real case study is used to illustrate the performance of the reviewed methods.
Download or read book Smoothing Spline ANOVA Models written by Chong Gu and published by Springer Science & Business Media. This book was released on 2013-01-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the ample computing power in today's servers, desktops, and laptops, smoothing methods have been finding their ways into everyday data analysis by practitioners. While scores of methods have proved successful for univariate smoothing, ones practical in multivariate settings number far less. Smoothing spline ANOVA models are a versatile family of smoothing methods derived through roughness penalties, that are suitable for both univariate and multivariate problems. In this book, the author presents a treatise on penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. The unifying themes are the general penalized likelihood method and the construction of multivariate models with built-in ANOVA decompositions. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source platform for statistical computing and graphics. Suites of functions are embodied in the R package gss, and are illustrated throughout the book using simulated and real data examples. This monograph will be useful as a reference work for researchers in theoretical and applied statistics as well as for those in other related disciplines. It can also be used as a text for graduate level courses on the subject. Most of the materials are accessible to a second year graduate student with a good training in calculus and linear algebra and working knowledge in basic statistical inferences such as linear models and maximum likelihood estimates.
Download or read book Smoothing Splines written by Yuedong Wang and published by CRC Press. This book was released on 2023-01-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many real-world examples, this book shows how to apply the powerful methods of smoothing splines in practice. It covers basic smoothing spline models as well as more advanced models, such as spline smoothing with correlated random errors. It also presents methods for model selection and inference. The author makes the advanced smoothing spl
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-09-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Download or read book Computationally Efficient Kalman Filter Approaches for Fitting Smoothing Splines written by Xiaoxiao Sun and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothing spline models have shown to be effective in various fields (e.g., engineering and biomedical sciences) for understanding complex signals from noisy data. As nonparametric models, smoothing spline ANOVA (Analysis Of variance) models do not fix the structure of the regression function, leading to more flexible model estimates (e.g., linear or nonlinear estimates). The functional ANOVA decomposition of the regression function estimates offers interpretable results that describe the relationship between the outcome variable, and the main and interaction effects of different covariates/predictors. However, smoothing spline ANOVA (SS-ANOVA) models suffer from high computational costs, with a computational complexity of ON3 for N observations. Various numerical approaches can address this problem. In this chapter, we focus on the introduction to a state space representation of SS-ANOVA models. The estimation algorithms based on the Kalman filter are implemented within the SS-ANOVA framework using the state space representation, reducing the computational costs significantly.
Download or read book Topics in Splines and Applications written by Young Kinh-Nhue Truong and published by BoD – Books on Demand. This book was released on 2018-06-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.
Download or read book Methods and Applications of Linear Models written by Ronald R. Hocking and published by Wiley-Interscience. This book was released on 2003-04-07 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular statistical text now updated and better than ever! The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved. Now in its second edition, Methods and Applications of Linear Models: Regression and the Analysis of Variance seeks to more effectively address the analysis of such models through several important changes. Notable in this new edition: Fully updated and expanded text reflects the most recent developments in the AVE method Rearranged and reorganized discussions of application and theory enhance text’s effectiveness as a teaching tool More than 100 new exercises in the areas of regression and analysis of variance As in the First Edition, the author presents a thorough treatment of the concepts and methods of linear model analysis, and illustrates them with various numerical and conceptual examples, using a data-based approach to development and analysis. Data sets, available on an FTP site, allow readers to apply analytical methods discussed in the book.
Download or read book Adaptive Basis Sampling for Smoothing Splines written by Nan Zhang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothing splines provide flexible nonparametric regression estimators. Penalized likelihood method is adopted when responses are from exponential families and multivariate models are constructed with certain analysis of variance decomposition. However, the high computational cost of smoothing splines for large data sets has hindered their wide application. We develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Generally, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is O(n3). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. We show that the proposed method outperforms a sampling method that does not use the values of response variable by simulation studies, and apply it to several real data examples. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155626
Download or read book System Identification 2003 written by Paul Van Den Hof and published by Elsevier. This book was released on 2004-06-29 with total page 2092 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of the symposium covers all major aspects of system identification, experimental modelling, signal processing and adaptive control, ranging from theoretical, methodological and scientific developments to a large variety of (engineering) application areas. It is the intention of the organizers to promote SYSID 2003 as a meeting place where scientists and engineers from several research communities can meet to discuss issues related to these areas. Relevant topics for the symposium program include: Identification of linear and multivariable systems, identification of nonlinear systems, including neural networks, identification of hybrid and distributed systems, Identification for control, experimental modelling in process control, vibration and modal analysis, model validation, monitoring and fault detection, signal processing and communication, parameter estimation and inverse modelling, statistical analysis and uncertainty bounding, adaptive control and data-based controller tuning, learning, data mining and Bayesian approaches, sequential Monte Carlo methods, including particle filtering, applications in process control systems, motion control systems, robotics, aerospace systems, bioengineering and medical systems, physical measurement systems, automotive systems, econometrics, transportation and communication systems *Provides the latest research on System Identification*Contains contributions written by experts in the field*Part of the IFAC Proceedings Series which provides a comprehensive overview of the major topics in control engineering.
Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2003 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Data Mining and Knowledge Discovery written by Hamparsum Bozdogan and published by CRC Press. This book was released on 2003-07-29 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Massive data sets pose a great challenge to many cross-disciplinary fields, including statistics. The high dimensionality and different data types and structures have now outstripped the capabilities of traditional statistical, graphical, and data visualization tools. Extracting useful information from such large data sets calls for novel approache
Download or read book Technometrics written by and published by . This book was released on 2003 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the International Conference on Hydrology and Water Resources New Delhi India December 1993 written by V.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Water is vital to life, maintenance of ecological balance, economic development, and sustenance of civilization. Planning and management of water resources and its optimal use are a matter of urgency for most countries of the world, and even more so for India with a huge population. Growing population and expanding economic activities exert increasing demands on water for varied needs--domestic, industrial, agricultural, power generation, navigation, recreation, etc. In India, agriculture is the highest user of water. The past three decades have witnessed numerous advances as well as have presented intriguing challenges and exciting opportunities in hydrology and water resources. Compounding them has been the growing environmental consciousness. Nowhere are these challenges more apparent than in India. As we approach the twenty first century, it is entirely fitting to take stock of what has been accomplished and what remains to be accomplished, and what accomplishments are relevant, with particular reference to Indian conditions.
Download or read book Generalized Additive Models written by Simon Wood and published by CRC Press. This book was released on 2006-02-27 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Current Index to Statistics Applications Methods and Theory written by and published by . This book was released on 1998 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Download or read book American Doctoral Dissertations written by and published by . This book was released on 2001 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
