Download or read book Variance Estimation for High Dimensional Regression Models written by Vladimir Spokoiny and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-05-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Download or read book High dimensional Econometrics And Identification written by Kao Chihwa and published by World Scientific. This book was released on 2019-04-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications of econometrics and economics, a large proportion of the questions of interest are identification. An economist may be interested in uncovering the true signal when the data could be very noisy, such as time-series spurious regression and weak instruments problems, to name a few. In this book, High-Dimensional Econometrics and Identification, we illustrate the true signal and, hence, identification can be recovered even with noisy data in high-dimensional data, e.g., large panels. High-dimensional data in econometrics is the rule rather than the exception. One of the tools to analyze large, high-dimensional data is the panel data model.High-Dimensional Econometrics and Identification grew out of research work on the identification and high-dimensional econometrics that we have collaborated on over the years, and it aims to provide an up-todate presentation of the issues of identification and high-dimensional econometrics, as well as insights into the use of these results in empirical studies. This book is designed for high-level graduate courses in econometrics and statistics, as well as used as a reference for researchers.
Download or read book Components of Variance written by D.R. Cox and published by CRC Press. This book was released on 2002-07-30 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The components of variance is a notion essential to statisticians and quantitative research scientists working in a variety of fields, including the biological, genetic, health, industrial, and psychological sciences. Co-authored by Sir David Cox, the pre-eminent statistician in the field, this book provides in-depth discussions that set forth the essential principles of the subject. It focuses on developing the models that form the basis for detailed analyses as well as on the statistical techniques themselves. The authors include a variety of examples from areas such as clinical trial design, plant and animal breeding, industrial design, and psychometrics.
Download or read book Local Variance Estimation for Uncensored and Censored Observations written by Paola Gloria Ferrario and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.
Download or read book Robust Statistical Procedures written by Peter J. Huber and published by SIAM. This book was released on 1996-01-01 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a brief, well-organized, and easy-to-follow introduction and overview of robust statistics. Huber focuses primarily on the important and clearly understood case of distribution robustness, where the shape of the true underlying distribution deviates slightly from the assumed model (usually the Gaussian law). An additional chapter on recent developments in robustness has been added and the reference list has been expanded and updated from the 1977 edition.
Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Download or read book Introduction to High Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2021-08-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
Download or read book Recursive Bias Estimation for High Dimensional Regression Smoothers written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In multivariate nonparametric analysis, sparseness of the covariates also called curse of dimensionality, forces one to use large smoothing parameters. This leads to biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting smoother has a small variance but a substantial bias. In this paper, we propose to iteratively correct of the bias initial estimator by an estimate of the latter obtained by smoothing the residuals. We examine in details the convergence of the iterated procedure for classical smoothers and relate our procedure to L2-Boosting, For multivariate thin plate spline smoother, we proved that our procedure adapts to the correct and unknown order of smoothness for estimating an unknown function m belonging to H([nu]) (Sobolev space where m should be bigger than d/2). We apply our method to simulated and real data and show that our method compares favorably with existing procedures.
Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Download or read book High dimensional Regression Models with Structured Coefficients written by Yuan Li and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression models are very common for statistical inference, especially linear regression models with Gaussian noise. But in many modern scientific applications with large-scale datasets, the number of samples is small relative to the number of model parameters, which is the so-called high- dimensional setting. Directly applying classical linear regression models to high-dimensional data is ill-posed. Thus it is necessary to impose additional assumptions for regression coefficients to make high-dimensional statistical analysis possible. Regularization methods with sparsity assumptions have received substantial attention over the past two decades. But there are still some open questions regarding high-dimensional statistical analysis. Firstly, most literature provides statistical analysis for high-dimensional linear models with Gaussian noise, it is unclear whether similar results still hold if we are no longer in the Gaussian setting. To answer this question under Poisson setting, we study the minimax rates and provide an implementable convex algorithm for high-dimensional Poisson inverse problems under weak sparsity assumption and physical constraints. Secondly, much of the theory and methodology for high-dimensional linear regression models are based on the assumption that independent variables are independent of each other or have weak correlations. But it is possible that this assumption is not satisfied that some features are highly correlated with each other. It is natural to ask whether it is still possible to make high-dimensional statistical inference with high-correlated designs. Thus we provide a graph-based regularization method for high-dimensional regression models with high-correlated designs along with theoretical guarantees.
Download or read book Modeling and Stochastic Learning for Forecasting in High Dimensions written by Anestis Antoniadis and published by Springer. This book was released on 2015-06-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume stress the need for advances in theoretical understanding to go hand-in-hand with the widespread practical application of forecasting in industry. Forecasting and time series prediction have enjoyed considerable attention over the last few decades, fostered by impressive advances in observational capabilities and measurement procedures. On June 5-7, 2013, an international Workshop on Industry Practices for Forecasting was held in Paris, France, organized and supported by the OSIRIS Department of Electricité de France Research and Development Division. In keeping with tradition, both theoretical statistical results and practical contributions on this active field of statistical research and on forecasting issues in a rapidly evolving industrial environment are presented. The volume reflects the broad spectrum of the conference, including 16 articles contributed by specialists in various areas. The material compiled is broad in scope and ranges from new findings on forecasting in industry and in time series, on nonparametric and functional methods and on on-line machine learning for forecasting, to the latest developments in tools for high dimension and complex data analysis.
Download or read book Linear and Generalized Linear Mixed Models and Their Applications written by Jiming Jiang and published by Springer Science & Business Media. This book was released on 2007-05-30 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book High Dimensional Statistics written by Martin J. Wainwright and published by Cambridge University Press. This book was released on 2019-02-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Download or read book U Statistics Mm Estimators and Resampling written by Arup Bose and published by Springer. This book was released on 2018-08-28 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.
Download or read book Computational Science ICCS 2024 written by Leonardo Franco and published by Springer Nature. This book was released on with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt:
