Download or read book Consistent Variable Selection Via Adaptive Diagonal Ridge Estimator in Regression Models written by Kim Minbok and published by . This book was released on 2008 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Consistent Bi level Variable Selection Via Composite Group Bridge Penalized Regression written by Indu Seetharaman and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the composite group bridge penalized regression methods for conducting bilevel variable selection in high dimensional linear regression models with a diverging number of predictors. The proposed method combines the ideas of bridge regression (Huang et al., 2008a) and group bridge regression (Huang et al., 2009), to achieve variable selection consistency in both individual and group levels simultaneously, i.e., the important groups and the important individual variables within each group can both be correctly identi ed with probability approaching to one as the sample size increases to in nity. The method takes full advantage of the prior grouping information, and the established bi-level oracle properties ensure that the method is immune to possible group misidenti cation. A related adaptive group bridge estimator, which uses adaptive penalization for improving bi-level selection, is also investigated. Simulation studies show that the proposed methods have superior performance in comparison to many existing methods.
Download or read book Adaptive Regression written by Yadolah Dodge and published by Springer Science & Business Media. This book was released on 2012-10-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there have been a large number of estimation methods proposed and developed for linear regression, none has proved good for all purposes. This text focuses on the construction of an adaptive combination of two estimation methods so as to help users make an objective choice and combine the desirable properties of two estimators.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 906 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book IMPROVING THE ACCURACY OF VARIABLE SELECTION USING THE WHOLE SOLUTION PATH written by Yang Liu and published by . This book was released on 2015 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The performances of penalized least squares approaches profoundly depend on the selection of the tuning parameter; however, statisticians did not reach consensus on the criterion for choosing the tuning parameter. Moreover, the penalized least squares estimation that based on a single value of the tuning parameter suffers from several drawbacks. The tuning parameter selected by the traditional selection criteria such as AIC, BIC, CV tends to pick excessive variables, which results in an over-fitting model. On the contrary, many other criteria, such as the extended BIC that favors an over-sparse model, may run the risk of dropping some relevant variables in the model. In the dissertation, a novel approach for the feature selection based on the whole solution paths is proposed, which significantly improves the selection accuracy. The key idea is to partition the variables into the relevant set and the irrelevant set at each tuning parameter, and then select the variables which have been classified as relevant for at least one tuning parameter. The approach is named as Selection by Partitioning the Solution Paths (SPSP). Compared with other existing feature selection approaches, the proposed SPSP algorithm allows feature selection by using a wide class of penalty functions, including Lasso, ridge and other strictly convex penalties. Based on the proposed SPSP procedure, a new type of scores are presented to rank the importance of the variables in the model. The scores, noted as Area-out-of-zero-region Importance Scores (AIS), are defined by the areas between the solution paths and the boundary of the partitions over the whole solution paths. By applying the proposed scores in the stepwise selection, the false positive error of the selection is remarkably reduced. The asymptotic properties for the proposed SPSP estimator have been well established. It is showed that the SPSP estimator is selection consistent when the original estimator is either estimation consistent or selection consistent. Specially, the SPSP approach on the Lasso has been proved to be consistent over the whole solution paths under the irrepresentable condition. Additionally, a number of simulation studies have been conducted to illustrate the performance of the proposed approachs. The comparison between the SPSP algorithm and the existing selection criteria on the Lasso, the adaptive Lasso, the SCAD and the MCP were provided. The results showed the proposed method outperformed the existing variable selection methods in general. Finally, two real data examples of identifying the informative variables in the Boston housing data and the glioblastoma gene expression data are given. Compared with the models selected by other existing approaches, the models selected by the SPSP procedure are much simpler with relatively smaller model errors.
Download or read book Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning written by Norbert Christopeit and published by . This book was released on 2010 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Simulation and Resampling Methods for Social Science written by Thomas M. Carsey and published by SAGE Publications. This book was released on 2013-08-05 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, this book examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.
Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 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 Linear Models in Statistics written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2008-01-07 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Download or read book Resampling Based Multiple Testing written by Peter H. Westfall and published by John Wiley & Sons. This book was released on 1993-01-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Download or read book Linear Regression Analysis written by Xin Yan and published by World Scientific. This book was released on 2009 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.
Download or read book Multivariate Statistical Machine Learning Methods for Genomic Prediction written by Osval Antonio Montesinos López and published by Springer Nature. This book was released on 2022-02-14 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.
Download or read book Econometric Analysis of Count Data written by Rainer Winkelmann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this book is to provide an introduction to the econometric modeling of count data for graduate students and researchers. It should serve anyone whose interest lies either in developing the field fur ther, or in applying existing methods to empirical questions. Much of the material included in this book is not specific to economics, or to quantita tive social sciences more generally, but rather extends to disciplines such as biometrics and technometrics. Applications are as diverse as the number of congressional budget vetoes, the number of children in a household, and the number of mechanical defects in a production line. The unifying theme is a focus on regression models in which a dependent count variable is modeled as a function of independent variables which mayor may not be counts as well. The modeling of count data has come of age. Inclusion of some of the fundamental models in basic textbooks, and implementation on standard computer software programs bear witness to that. Based on the standard Poisson regression model, numerous extensions and alternatives have been developed to address the common challenges faced in empirical modeling (unobserved heterogeneity, selectivity, endogeneity, measurement error, and dependent observations in the context of panel data or multivariate data, to name but a few) as well as the challenges that are specific to count data (e. g. , over dispersion and underdispersion).
Download or read book Gaussian Process Regression Analysis for Functional Data written by Jian Qing Shi and published by CRC Press. This book was released on 2011-07-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Coveri
Download or read book Parameter Estimation in Engineering and Science written by James Vere Beck and published by James Beck. This book was released on 1977 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to and survey of parameter estimation; Probability; Introduction to statistics; Parameter estimation methods; Introduction to linear estimation; Matrix analysis for linear parameter estimation; Minimization of sum of squares functions for models nonlinear in parameters; Design of optimal experiments.
Download or read book Modeling Ordered Choices written by William H. Greene and published by Cambridge University Press. This book was released on 2010-04-08 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is increasingly common for analysts to seek out the opinions of individuals and organizations using attitudinal scales such as degree of satisfaction or importance attached to an issue. Examples include levels of obesity, seriousness of a health condition, attitudes towards service levels, opinions on products, voting intentions, and the degree of clarity of contracts. Ordered choice models provide a relevant methodology for capturing the sources of influence that explain the choice made amongst a set of ordered alternatives. The methods have evolved to a level of sophistication that can allow for heterogeneity in the threshold parameters, in the explanatory variables (through random parameters), and in the decomposition of the residual variance. This book brings together contributions in ordered choice modeling from a number of disciplines, synthesizing developments over the last fifty years, and suggests useful extensions to account for the wide range of sources of influence on choice.
