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Sparse Linear Models And L1 Regularized 2sls With High Dimensional Endogenous Regressors And Instruments
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Book Synopsis Sparse Linear Models and L1-Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments by : Ying Zhu
Download or read book Sparse Linear Models and L1-Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments written by Ying Zhu and published by . This book was released on 2018 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We explore the validity of the 2-stage least squares estimator with l_{1}-regularization in both stages, for linear triangular models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression coefficients are sufficiently sparse. For this l_{1}-regularized 2-stage least squares estimator, we first establish finite-sample performance bounds and then provide a simple practical method (with asymptotic guarantees) for choosing the regularization parameter. We also sketch an inference strategy built upon this practical method.
Book Synopsis L1-Penalized Quantile Regression in High Dimensional Sparse Models by : Victor Chernozhukov
Download or read book L1-Penalized Quantile Regression in High Dimensional Sparse Models written by Victor Chernozhukov and published by . This book was released on 2009 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of the response variable, where s grows slower than n. Since in this case the ordinary quantile regression is not consistent, we consider quantile regression penalized by the 1-norm of coefficients (L1-QR). First, we show that L1-QR is consistent, up to a logarithmic factor, at the oracle rate which is achievable when the minimal true model is known. The overall number of regressors p affects the rate only through a logarithmic factor, thus allowing nearly exponential growth in the number of zero-impact regressors. The rate result holds under relatively weak conditions, requiring that s/n converges to zero at a super-logarithmic speed and that regularization parameter satisfies certain theoretical constraints. Second, we propose a pivotal, data-driven choice of the regularization parameter and show that it satisfies these theoretical constraints. Third, we show that L1-QR correctly selects the true minimal model as a valid submodel, when the non-zero coefficients of the true model are well separated from zero. We also show that the number of non-zero coefficients in L1-QR is of same stochastic order as s, the number of non-zero coefficients in the minimal true model. Fourth, we analyze the rate of convergence of a two-step estimator that applies ordinary quantile regression to the selected model. Fifth, we evaluate the performance of L1-QR in a Monte-Carlo experiment, and provide an application to the analysis of the international economic growth. Keywords: median regression, quantile regression, sparse models. JEL Classifications: C13, C14, C30, C51, D4, J24, J31.
Book Synopsis Post-selection and Post-regularization Inference Linear Models with Very Many Controls and Instruments by : Victor Chernozhukov
Download or read book Post-selection and Post-regularization Inference Linear Models with Very Many Controls and Instruments written by Victor Chernozhukov and published by . This book was released on 2015 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this note, we offer an approach to estimating structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The approach we take extends Belloni et al. (2012), which covers selection of instruments for IV models with a small number of controls, and extends Belloni, Chernozhukov and Hansen (2014), which covers selection of controls in models where the variable of interest is exogenous conditional on observables, to accommodate both a large number of controls and a large number of instruments. We illustrate the approach with a simulation and an empirical example. Technical supporting material is available in a supplementary appendix.
Book Synopsis Statistical Inference for High-Dimensional Linear Models by : Zijian Guo
Download or read book Statistical Inference for High-Dimensional Linear Models written by Zijian Guo and published by . This book was released on 2017 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional linear models play an important role in the analysis of modern data sets. Although the estimation problem has been well understood, there is still a paucity of methods and theories on the inference problem for high-dimensional linear models. This thesis focuses on statistical inference for high-dimensional linear models and consists of the following three parts. 1. The first part of the thesis considers confidence intervals for linear functionals in high-dimensional linear regression. We first establish the convergence rates of the minimax expected length for confidence intervals. Furthermore, we investigate the problem of adaptation to sparsity for the construction of confidence intervals and identify the regimes in which it is possible to construct adaptive confidence intervals. 2. In the second part of the thesis, we consider point and interval estimation of the lq loss of a given estimator in high-dimensional linear regression. For the class of rate-optimal estimators, we establish the minimax rates for estimating their lq losses, the minimax expected length of confidence intervals for their lq losses and the possibility of adaptivity of confidence intervals for their lq losses. 3. In the third part of the thesis, we consider the problem in the framework of high-dimensional instrumental variable regression and construct confidence intervals for the treatment effect in the presence of possibly invalid instrumental variables. We develop a novel selection procedure, Two-Stage Hard Thresholding (TSHT) to select valid instrumental variables and construct honest confidence intervals for the treatment effect using the selected instrumental variables.
Book Synopsis TWO STEPWISE REGRESSION METHODS AND CONSISTENT MODEL SELECTION FOR HIGHLY CORRELATED AND HIGH-DIMENSIONAL SPARSE LINEAR MODELS. by : Yuan-Yi Fu
Download or read book TWO STEPWISE REGRESSION METHODS AND CONSISTENT MODEL SELECTION FOR HIGHLY CORRELATED AND HIGH-DIMENSIONAL SPARSE LINEAR MODELS. written by Yuan-Yi Fu and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boosting Methods for Variable Selection in High Dimensional Sparse Models by :
Download or read book Boosting Methods for Variable Selection in High Dimensional Sparse Models written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Firstly, we propose new variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work better for an extremely sparse high dimensional linear regression model. We exploit the fact that the LASSO, adaptive LASSO and elastic net have closed form solutions when the predictor is one-dimensional. The explicit formula is then repeatedly used in an iterative fashion until convergence occurs. By carefully considering the relationship between estimators at successive stages, we develop fast algorithms to compute our estimators. The performance of our new estimators is compared with commonly used estimators in terms of predictive accuracy and errors in variable selection. It is observed that our approach has better prediction performance for highly sparse high dimensional linear regression models. Secondly, we propose a new variable selection technique for binary classification in high dimensional models based on a forward selection version of the Squared Support Vector Machines or one-norm Support Vector Machines, to be called as forward iterative selection and classification algorithm (FISCAL). This methods seem to work better for a highly sparse high dimensional binary classification model. We suggest the squared support vector machines using 1-norm and 2-norm simultaneously. The squared support vector machines are convex and differentiable except at zero when the predictor is one-dimensional. Then an iterative forward selection approach is applied along with the squared support vector machines until a stopping rule is satisfied. Also, we develop a recursive algorithm for the FISCAL to save computational burdens. We apply the processes to the original onenorm Support Vector Machines. We compare the FISCAL with other widely used.
Book Synopsis Human Microbiome in Health and Disease - Part A by :
Download or read book Human Microbiome in Health and Disease - Part A written by and published by Academic Press. This book was released on 2022-09-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Human Microbiome in Health and Disease, Volume 191, Part A presents updated knowledge on human microbiome as covered by renowned science faculty across the globe. Chapters in this volume include an introduction to human microbiome, Structure, functions and diversity of healthy human microbiome, Role of human microbiome in cancer, Gut microbiota and gastrointestinal cancer, Dysbiosis of human microbiome and metabolic diseases, Gut microbiome and type 2 diabetes, Gut microbiome and non-alcoholic fatty liver disease, Hepatic drug metabolism and intestinal microbiota, Emerging tools for understanding the human microbiome, and Microbiome therapeutics: Opportunity and challenges, and more. These chapters cover the composition, diversity, dynamics and functions of human microbiome in health and disease. This book will form an excellent and informative text on keystone, autochthonous, and exogenous microbiota important for human health in a simple to understand and easy to read format.
Download or read book Model Averaging written by David Fletcher and published by Springer. This book was released on 2019-01-17 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Book Synopsis The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics by : Jeffrey Racine
Download or read book The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics written by Jeffrey Racine and published by Oxford University Press. This book was released on 2014-04 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures.
Book Synopsis Structural Equation Models by : J. Christopher Westland
Download or read book Structural Equation Models written by J. Christopher Westland and published by Springer. This book was released on 2015-04-25 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact reference surveys the full range of available structural equation modeling (SEM) methodologies. It reviews applications in a broad range of disciplines, particularly in the social sciences where many key concepts are not directly observable. This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method. This book also surveys the emerging path and network approaches that complement and enhance SEM, and that will grow importance in the near future. SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists. Latent variable theory and application are comprehensively explained and methods are presented for extending their power, including guidelines for data preparation, sample size calculation and the special treatment of Likert scale data. Tables of software, methodologies and fit statistics provide a concise reference for any research program, helping assure that its conclusions are defensible and publishable.
Download or read book Econometrics written by Bruce Hansen and published by Princeton University Press. This book was released on 2022-08-16 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most authoritative and up-to-date core econometrics textbook available Econometrics is the quantitative language of economic theory, analysis, and empirical work, and it has become a cornerstone of graduate economics programs. Econometrics provides graduate and PhD students with an essential introduction to this foundational subject in economics and serves as an invaluable reference for researchers and practitioners. This comprehensive textbook teaches fundamental concepts, emphasizes modern, real-world applications, and gives students an intuitive understanding of econometrics. Covers the full breadth of econometric theory and methods with mathematical rigor while emphasizing intuitive explanations that are accessible to students of all backgroundsDraws on integrated, research-level datasets, provided on an accompanying websiteDiscusses linear econometrics, time series, panel data, nonparametric methods, nonlinear econometric models, and modern machine learningFeatures hundreds of exercises that enable students to learn by doingIncludes in-depth appendices on matrix algebra and useful inequalities and a wealth of real-world examplesCan serve as a core textbook for a first-year PhD course in econometrics and as a follow-up to Bruce E. Hansen’s Probability and Statistics for Economists
Book Synopsis Functional Data Analysis by : James Ramsay
Download or read book Functional Data Analysis written by James Ramsay and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.
Book Synopsis Identification and Inference for Econometric Models by : Donald W. K. Andrews
Download or read book Identification and Inference for Econometric Models written by Donald W. K. Andrews and published by Cambridge University Press. This book was released on 2005-06-17 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 collection pushed forward the research frontier in four areas of theoretical econometrics.
Book Synopsis Fixed-Point Algorithms for Inverse Problems in Science and Engineering by : Heinz H. Bauschke
Download or read book Fixed-Point Algorithms for Inverse Problems in Science and Engineering written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Book Synopsis In Defence of Labour Market Institutions by : J. Berg
Download or read book In Defence of Labour Market Institutions written by J. Berg and published by Springer. This book was released on 2008-02-22 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though labour market regulations have been blamed for the poor economic performance of many developing countries, the evidence on which this argument rests is weak. Through a survey of different labour market institutions in developing countries, this book reaffirms the importance of labour market institutions in this era of globalization.
Book Synopsis Theory of Ridge Regression Estimation with Applications by : A. K. Md. Ehsanes Saleh
Download or read book Theory of Ridge Regression Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2019-01-08 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.
Book Synopsis The Foundations of Econometric Analysis by : David F. Hendry
Download or read book The Foundations of Econometric Analysis written by David F. Hendry and published by Cambridge University Press. This book was released on 1997-02-20 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of classic papers by pioneer econometricians
