Download or read book Forecasting with Sufficient Dimension Reductions written by Alessandro Barbarino and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Moment Methods for Sufficient Forecasting Using High Dimensional Predictors written by Wei Luo and published by . This book was released on 2017 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider forecasting a single time series using high-dimensional predictors in the presence of a possible nonlinear forecast function. The sufficient forecasting (Fan et al., 2016) used sliced inverse regression to estimate lower-dimensional sufficient indices for non-parametric forecasting using factor models. However, Fan et al. (2016) is fundamentally limited to the inverse first-moment method, by assuming the restricted fixed number of factors, linearity condition for factors, and monotone effect of factors on the response. In this work, we study the inverse second-moment method using directional regression and the inverse third-moment method to extend the methodology and applicability of the sufficient forecasting. As the number of factors diverges with the dimension of predictors, the proposed method relaxes the distributional assumption of the predictor and enhances the capability of capturing the non-monotone effect of factors on the response. We not only provide a high-dimensional analysis of inverse moment methods such as exhaustiveness and rate of convergence, but also prove their model selection consistency. The power of our proposed methods is demonstrated in both simulation studies and an empirical study of forecasting monthly macroeconomic data from Q1 1959 to Q1 2016. During our theoretical development, we prove an invariance result for inverse moment methods, which make a separate contribution to the sufficient dimension reduction.
Download or read book Sufficient Forecasting Using Factor Models written by Jianqing Fan and published by . This book was released on 2015 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional factor model implemented by the principal component analysis. Using the extracted factors, we develop a link-free forecasting method, called the sufficient forecasting, which provides several sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. Our method is also applicable to cross-sectional sufficient regression using extracted factors. {The connection between the sufficient forecasting and the deep learning architecture is explicitly stated.} The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We also show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.
Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.
Download or read book Advances in Business and Management Forecasting written by Kenneth D. Lawrence and published by Emerald Group Publishing. This book was released on 2019-09-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 13 of Advances in Business and Management Forecasting presents state-of-the-art studies in the application of forecasting methodologies to areas such as sales forecasting, retailing, service contracts, bankruptcy prediction, executive compensation, and call center staffing.
Download or read book Model Free Variable Selection Through Sufficient Dimension Reduction written by Angela Minster and published by . This book was released on 2016 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we draw upon the natural connection between the fields of sufficient dimension reduction and variable selection to develop new theory and methods for model-free variable selection. After developing the natural connection between sufficient dimension reduction and model-free variable selection we introduce two approaches to select independent variables important to predicting the response variable without making any assumptions about the function form of the relationship between predictor and response. The first is a stepwise procedure and the second takes a penalized approach. Both are rooted in ordinary least squares regression but with modifications to facilitate model-free variable selection. We also introduce a set of transformations for model-free variable selection. Finally we develop a stepwise procedure that is able to select interaction terms in the model-free setting. We show the effectiveness of these methods through simulation studies and an analysis of real data.
Download or read book Forecasting Financial and Macroeconomic Variables written by and published by . This book was released on 2014 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sufficient Dimension Reduction Based on Normal and Wishart Inverse Models written by Liliana Forzani and published by . This book was released on 2007 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Integrative Sufficient Dimension Reduction Method for Multi omics Data Analysis written by Yashita Jain and published by . This book was released on 2017 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advancement in next-generation sequencing, transcriptomics, proteomics andother high-throughput technologies has enabled to simultaneously measure multipletypes of genomic data for cancer samples. These data may reveal new biological in-sights as compared to analyzing one single genome type. This study proposes a newintegrative supervised dimension reduction method, called integrative sliced inverseregression (integrative SIR), for simultaneous analysis of multiple omics data types ofcancer samples, including MiRNA, MRNA and proteomics, to improve prediction andinterpretation. The proposed method can reduce the dimensions of multiple omics datasimultaneously while sharing common latent structures without losing any informationin prediction. By capturing common information across data types, the new methoddemonstrates advantages over conventional methods. In this work, we classify differenttumor types like CNS, leukemia and melanoma using dimension reduction methods.
Download or read book Nonparametric Estimation of Conditional Expectation with Auxiliary Information and Dimension Reduction written by Bingying Xie and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric estimation of the conditional expectation E(Y|U)) of an outcome Y given a covariate vector U is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable Z in the training dataset used to construct estimators. But Z is not available for future prediction or analysis in personalized medicine. For example, in the training dataset the outcome is longitudinal, but only the end point Y is concerned in the future prediction or analysis. The longitudinal outcomes other than the end point is then the variable Z that is observed and related with both Y and U. Previous work on how to make use of Z in the estimation of E(Y|U)) mainly focused on using Z in the construction of a linear function of U to reduce covariate dimension for better estimation. Using E(Y|U)) = E{E(Y|U), Z)|U}, we propose a two-step estimation of inner and outer expectations, respectively, with sufficient dimension reduction for kernel estimation in both steps. The information Z is utilized not only in dimension reduction, but also directly in the estimation. Because of the existence of different ways for dimension reduction, we construct two estimators that may improve the estimator without using Z. The improvements are shown in the convergence rate of estimators as the sample size increases to infinity as well as in the finite sample simulation performance. A real data analysis about the selection of mammography intervention is presented for illustration.
Download or read book Elements of Dimensionality Reduction and Manifold Learning written by Benyamin Ghojogh and published by Springer Nature. This book was released on 2023-02-02 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimensionality reduction, also known as manifold learning, is an area of machine learning used for extracting informative features from data for better representation of data or separation between classes. This book presents a cohesive review of linear and nonlinear dimensionality reduction and manifold learning. Three main aspects of dimensionality reduction are covered: spectral dimensionality reduction, probabilistic dimensionality reduction, and neural network-based dimensionality reduction, which have geometric, probabilistic, and information-theoretic points of view to dimensionality reduction, respectively. The necessary background and preliminaries on linear algebra, optimization, and kernels are also explained to ensure a comprehensive understanding of the algorithms. The tools introduced in this book can be applied to various applications involving feature extraction, image processing, computer vision, and signal processing. This book is applicable to a wide audience who would like to acquire a deep understanding of the various ways to extract, transform, and understand the structure of data. The intended audiences are academics, students, and industry professionals. Academic researchers and students can use this book as a textbook for machine learning and dimensionality reduction. Data scientists, machine learning scientists, computer vision scientists, and computer scientists can use this book as a reference. It can also be helpful to statisticians in the field of statistical learning and applied mathematicians in the fields of manifolds and subspace analysis. Industry professionals, including applied engineers, data engineers, and engineers in various fields of science dealing with machine learning, can use this as a guidebook for feature extraction from their data, as the raw data in industry often require preprocessing. The book is grounded in theory but provides thorough explanations and diverse examples to improve the reader’s comprehension of the advanced topics. Advanced methods are explained in a step-by-step manner so that readers of all levels can follow the reasoning and come to a deep understanding of the concepts. This book does not assume advanced theoretical background in machine learning and provides necessary background, although an undergraduate-level background in linear algebra and calculus is recommended.
Download or read book Regression Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of regression graphics through computer graphics. Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory. Other important features of this book include: * Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots * Graphical regression, an iterative visualization process for constructing sufficient regression views * Graphics for regressions with a binary response * Graphics for model assessment, including residual plots * Net-effects plots for assessing predictor contributions * Graphics for predictor and response transformations * Inverse regression methods * Access to a Web site of supplemental plots, data sets, and 3D color displays. An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians.
Download or read book An Introduction to Envelopes written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2018-09-07 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods An Introduction to Envelopes provides an overview of the theory and methods of envelopes, a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives. The author offers a balance between foundations and methodology by integrating illustrative examples that show how envelopes can be used in practice. He discusses how to use envelopes to target selected coefficients and explores predictor envelopes and their connection with partial least squares regression. The book reveals the potential for envelope methodology to improve estimation of a multivariate mean. The text also includes information on how envelopes can be used in generalized linear models, regressions with a matrix-valued response, and reviews work on sparse and Bayesian response envelopes. In addition, the text explores relationships between envelopes and other dimension reduction methods, including canonical correlations, reduced-rank regression, supervised singular value decomposition, sufficient dimension reduction, principal components, and principal fitted components. This important resource: • Offers a text written by the leading expert in this field • Describes groundbreaking work that puts the focus on this burgeoning area of study • Covers the important new developments in the field and highlights the most important directions • Discusses the underlying mathematics and linear algebra • Includes an online companion site with both R and Matlab support Written for researchers and graduate students in multivariate analysis and dimension reduction, as well as practitioners interested in statistical methodology, An Introduction to Envelopes offers the first book on the theory and methods of envelopes.
Download or read book Multivariate Time Series Analysis and Applications written by William W. S. Wei and published by John Wiley & Sons. This book was released on 2019-03-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis—Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.
Download or read book Proceedings of the Tenth International Conference on Management Science and Engineering Management written by Jiuping Xu and published by Springer. This book was released on 2016-08-23 with total page 1697 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the Tenth International Conference on Management Science and Engineering Management (ICMSEM2016) held from August 30 to September 02, 2016 at Baku, Azerbaijan and organized by the International Society of Management Science and Engineering Management, Sichuan University (Chengdu, China) and Ministry of Education of Azerbaijan. The aim of conference was to foster international research collaborations in management science and engineering management as well as to provide a forum to present current research findings. The presented papers were selected and reviewed by the Program Committee, made up of respected experts in the area of management science and engineering management from around the globe. The contributions focus on identifying management science problems in engineering, innovatively using management theory and methods to solve engineering problems effectively and establishing novel management theories and methods to address new engineering management issues.
Download or read book Software Engineering and Computer Systems Part II written by Jasni Mohamad Zain and published by Springer Science & Business Media. This book was released on 2011-06-22 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Three-Volume-Set constitutes the refereed proceedings of the Second International Conference on Software Engineering and Computer Systems, ICSECS 2011, held in Kuantan, Malaysia, in June 2011. The 190 revised full papers presented together with invited papers in the three volumes were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on software engineering; network; bioinformatics and e-health; biometrics technologies; Web engineering; neural network; parallel and distributed e-learning; ontology; image processing; information and data management; engineering; software security; graphics and multimedia; databases; algorithms; signal processing; software design/testing; e- technology; ad hoc networks; social networks; software process modeling; miscellaneous topics in software engineering and computer systems.
Download or read book Demographic Forecasting written by Federico Girosi and published by Princeton University Press. This book was released on 2018-06-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demographic Forecasting introduces new statistical tools that can greatly improve forecasts of population death rates. Mortality forecasting is used in a wide variety of academic fields, and for policymaking in global health, social security and retirement planning, and other areas. Federico Girosi and Gary King provide an innovative framework for forecasting age-sex-country-cause-specific variables that makes it possible to incorporate more information than standard approaches. These new methods more generally make it possible to include different explanatory variables in a time-series regression for each cross section while still borrowing strength from one regression to improve the estimation of all. The authors show that many existing Bayesian models with explanatory variables use prior densities that incorrectly formalize prior knowledge, and they show how to avoid these problems. They also explain how to incorporate a great deal of demographic knowledge into models with many fewer adjustable parameters than classic Bayesian approaches, and develop models with Bayesian priors in the presence of partial prior ignorance. By showing how to include more information in statistical models, Demographic Forecasting carries broad statistical implications for social scientists, statisticians, demographers, public-health experts, policymakers, and industry analysts. Introduces methods to improve forecasts of mortality rates and similar variables Provides innovative tools for more effective statistical modeling Makes available free open-source software and replication data Includes full-color graphics, a complete glossary of symbols, a self-contained math refresher, and more
