Author: Son NguyenPublisher:
ISBN:
Category : Dimension reduction (Statistics)
Languages : en
Pages :
Book Description
Topics on Sufficient Dimension Reduction
Author: Son NguyenPublisher:
ISBN:
Category : Dimension reduction (Statistics)
Languages : en
Pages :
Book Description
Sufficient Dimension Reduction
Author: Bing LiPublisher: CRC Press
ISBN: 1351645730
Category : Mathematics
Languages : en
Pages : 362
Book Description
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.
Topics in Dimension Reduction
Author: Yongwu ShaoTopics on Supervised and Unsupervised Dimension Reduction
Author: Andreas A. ArtemiouTopics in Applied Statistics
Author: Mingxiu HuPublisher: Springer Science & Business Media
ISBN: 1461478464
Category : Medical
Languages : en
Pages : 340
Book Description
This volume presents 27 selected papers in topics that range from statistical applications in business and finance to applications in clinical trials and biomarker analysis. All papers feature original, peer-reviewed content. The editors intentionally selected papers that cover many topics so that the volume will serve the whole statistical community and a variety of research interests. The papers represent select contributions to the 21st ICSA Applied Statistics Symposium. The International Chinese Statistical Association (ICSA) Symposium took place between the 23rd and 26th of June, 2012 in Boston, Massachusetts. It was co-sponsored by the International Society for Biopharmaceutical Statistics (ISBS) and American Statistical Association (ASA). This is the inaugural proceedings volume to share research from the ICSA Applied Statistics Symposium.
Topics in Nonparametric Statistics
Author: Michael G. AkritasPublisher: Springer
ISBN: 1493905694
Category : Mathematics
Languages : en
Pages : 369
Book Description
This volume is composed of peer-reviewed papers that have developed from the First Conference of the International Society for Non Parametric Statistics (ISNPS). This inaugural conference took place in Chalkidiki, Greece, June 15-19, 2012. It was organized with the co-sponsorship of the IMS, the ISI and other organizations. M.G. Akritas, S.N. Lahiri and D.N. Politis are the first executive committee members of ISNPS and the editors of this volume. ISNPS has a distinguished Advisory Committee that includes Professors R.Beran, P.Bickel, R. Carroll, D. Cook, P. Hall, R. Johnson, B. Lindsay, E. Parzen, P. Robinson, M. Rosenblatt, G. Roussas, T. SubbaRao and G. Wahba. The Charting Committee of ISNPS consists of more than 50 prominent researchers from all over the world. The chapters in this volume bring forth recent advances and trends in several areas of nonparametric statistics. In this way, the volume facilitates the exchange of research ideas, promotes collaboration among researchers from all over the world and contributes to the further development of the field. The conference program included over 250 talks, including special invited talks, plenary talks and contributed talks on all areas of nonparametric statistics. Out of these talks, some of the most pertinent ones have been refereed and developed into chapters that share both research and developments in the field.
Sufficient Dimension Reduction and Variable Selection
Author: Xin ChenAnalysis of Sparse Sufficient Dimension Reduction Models
Author: Yeshan WithanagePublisher:
ISBN:
Category : Dimension reduction (Statistics)
Languages : en
Pages : 0
Book Description
Sufficient dimension reduction (SDR) in regression analysis with response variable y and predictor vector x is focused on reducing the dimension of x to a small number of linear combinations of the components in x. Since the introduction of the inverse regression method, SDR became a very active topic in the literature. When the dimension p of x is increasing with the number of observations n, the traditional SDR methods may not perform well. The purpose of this study is two fold, theoretical and empirical. In the theoretical analysis, I provide a proof for the consistency of a variable selection procedure in sparse single-index models (a special SDR model) through an inverse regression method called CUME. And for the case of multiple linear regression, I obtain the influence functions for estimators of the parameter vector with SCAD and MCP penalties by extending the idea of LASSO influence function. In the empirical aspect, I combine the LASSO-SIR algorithm with the influence function of LASSO to construct a new metric for choosing the penalty parameter for variable selection as an alternative approach to the usual cross-validation method. From the empirical analysis, it was found that the newly proposed influence function-based measure outperforms the traditional cross-validation method in a wide range of settings. Finally, I also propose an algorithm to estimate the structural dimension d of SDR models with large dimension p
Statistical Methods for Handling Incomplete Data
Author: Jae Kwang KimPublisher: CRC Press
ISBN: 1000466299
Category : Mathematics
Languages : en
Pages : 380
Book Description
Due to recent theoretical findings and advances in statistical computing, there has been a rapid development of techniques and applications in the area of missing data analysis. Statistical Methods for Handling Incomplete Data covers the most up-to-date statistical theories and computational methods for analyzing incomplete data. Features Uses the mean score equation as a building block for developing the theory for missing data analysis Provides comprehensive coverage of computational techniques for missing data analysis Presents a rigorous treatment of imputation techniques, including multiple imputation fractional imputation Explores the most recent advances of the propensity score method and estimation techniques for nonignorable missing data Describes a survey sampling application Updated with a new chapter on Data Integration Now includes a chapter on Advanced Topics, including kernel ridge regression imputation and neural network model imputation The book is primarily aimed at researchers and graduate students from statistics, and could be used as a reference by applied researchers with a good quantitative background. It includes many real data examples and simulated examples to help readers understand the methodologies.
Dimension Reduction
Author: Christopher J. C. BurgesPublisher: Now Publishers Inc
ISBN: 1601983786
Category : Computers
Languages : en
Pages : 104
Book Description
We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although the review focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nystr m method, which links several of the manifold algorithms, is also reviewed. We use a publicly available dataset to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.