L1 Penalized Quantile Regression In High Dimensional Sparse Models

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L1-Penalized Quantile Regression in High Dimensional Sparse Models

Author : Victor Chernozhukov
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (671 download)

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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.

Handbook of Quantile Regression

Author : Roger Koenker
Publisher : CRC Press
ISBN 13 : 1351646567
Total Pages : 739 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Quantile Regression by : Roger Koenker

Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

Inverse Problems and High-Dimensional Estimation

Author : Pierre Alquier
Publisher : Springer Science & Business Media
ISBN 13 : 3642199895
Total Pages : 204 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Inverse Problems and High-Dimensional Estimation by : Pierre Alquier

Download or read book Inverse Problems and High-Dimensional Estimation written by Pierre Alquier and published by Springer Science & Business Media. This book was released on 2011-06-07 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The “Stats in the Château” summer school was held at the CRC château on the campus of HEC Paris, Jouy-en-Josas, France, from August 31 to September 4, 2009. This event was organized jointly by faculty members of three French academic institutions ─ ENSAE ParisTech, the Ecole Polytechnique ParisTech, and HEC Paris ─ which cooperate through a scientific foundation devoted to the decision sciences. The scientific content of the summer school was conveyed in two courses, one by Laurent Cavalier (Université Aix-Marseille I) on "Ill-posed Inverse Problems", and one by Victor Chernozhukov (Massachusetts Institute of Technology) on "High-dimensional Estimation with Applications to Economics". Ten invited researchers also presented either reviews of the state of the art in the field or of applications, or original research contributions. This volume contains the lecture notes of the two courses. Original research articles and a survey complement these lecture notes. Applications to economics are discussed in various contributions.

Advances in Economics and Econometrics: Volume 3, Econometrics

Author : Daron Acemoglu
Publisher : Cambridge University Press
ISBN 13 : 1107717825
Total Pages : 633 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Advances in Economics and Econometrics: Volume 3, Econometrics by : Daron Acemoglu

Download or read book Advances in Economics and Econometrics: Volume 3, Econometrics written by Daron Acemoglu and published by Cambridge University Press. This book was released on 2013-05-13 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third of three volumes containing edited versions of papers and commentaries presented at invited symposium sessions of the Tenth World Congress of the Econometric Society, held in Shanghai in August 2010. The papers summarize and interpret key developments in economics and econometrics, and they discuss future directions for a wide variety of topics, covering both theory and application. Written by the leading specialists in their fields, these volumes provide a unique, accessible survey of progress on the discipline. The first volume primarily addresses economic theory, with specific focuses on nonstandard markets, contracts, decision theory, communication and organizations, epistemics and calibration, and patents.

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Author : Stephen Boyd
Publisher : Now Publishers Inc
ISBN 13 : 160198460X
Total Pages : 138 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers by : Stephen Boyd

Download or read book Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers written by Stephen Boyd and published by Now Publishers Inc. This book was released on 2011 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.

Advances in Economics and Econometrics

Author : Econometric Society. World Congress
Publisher : Cambridge University Press
ISBN 13 : 1107016061
Total Pages : 633 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Advances in Economics and Econometrics by : Econometric Society. World Congress

Download or read book Advances in Economics and Econometrics written by Econometric Society. World Congress and published by Cambridge University Press. This book was released on 2013-05-27 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume of edited papers from the Tenth World Congress of the Econometric Society 2010.

The Econometrics of Networks

Author : Áureo de Paula
Publisher : Emerald Group Publishing
ISBN 13 : 1838675779
Total Pages : 353 pages
Book Rating : 4.8/5 (386 download)

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Book Synopsis The Econometrics of Networks by : Áureo de Paula

Download or read book The Econometrics of Networks written by Áureo de Paula and published by Emerald Group Publishing. This book was released on 2020-10-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Showcasing fresh methodological and empirical research on the econometrics of networks, and comprising both theoretical, empirical and policy papers, the authors in this volume bring together a wide range of perspectives to facilitate a dialogue between academics and practitioners for better understanding this groundbreaking field.

Valid Post-selection Inference in High-dimensional Approximately Sparse Quantile Regression Models

Author : Alexandre Belloni
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (931 download)

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Book Synopsis Valid Post-selection Inference in High-dimensional Approximately Sparse Quantile Regression Models by : Alexandre Belloni

Download or read book Valid Post-selection Inference in High-dimensional Approximately Sparse Quantile Regression Models written by Alexandre Belloni and published by . This book was released on 2014 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work proposes new inference methods for the estimation of a regression coefficient of interest in quantile regression models. We consider high-dimensional models where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable approximation of the unknown quantile regression function in the model. The proposed methods are protected against moderate model selection mistakes, which are often inevitable in the approximately sparse model considered here. The methods construct (implicitly or explicitly) an optimal instrument as a residual from a density-weighted projection of the regressor of interest on other regressors. Under regularity conditions, the proposed estimators of the quantile regression coefficient are asymptotically root-n normal, with variance equal to the semi-parametric efficiency bound of the partially linear quantile regression model. In addition, the performance of the technique is illustrated through Monte-carlo experiments and an empirical example, dealing with risk factors in childhood malnutrition. The numerical results confirm the theoretical findings that the proposed methods should outperform the naive post-model selection methods in non-parametric settings. Moreover, the empirical results demonstrate soundness of the proposed methods.

Discovery Science

Author : Jean-Gabriel Ganascia
Publisher : Springer
ISBN 13 : 364233492X
Total Pages : 341 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Discovery Science by : Jean-Gabriel Ganascia

Download or read book Discovery Science written by Jean-Gabriel Ganascia and published by Springer. This book was released on 2012-10-22 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Conference on Discovery Science, DS 2012, held in Lyon, France, in October 2012. The 22 papers presented in this volume were carefully reviewed and selected from 46 submissions. The field of discovery science aims at inducing and validating new scientific hypotheses from data. The scope of this conference includes the development and analysis of methods for automatic scientific knowledge discovery, machine learning, intelligent data analysis, theory of learning, tools for supporting the human process of discovery in science, as well as their application to knowledge discovery.

Penalized Model Averaging for High Dimensional Quantile Regressions

Author : Haowen Bao
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Penalized Model Averaging for High Dimensional Quantile Regressions by : Haowen Bao

Download or read book Penalized Model Averaging for High Dimensional Quantile Regressions written by Haowen Bao and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Statistical Foundations of Data Science

Author : Jianqing Fan
Publisher : CRC Press
ISBN 13 : 1466510854
Total Pages : 752 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Statistical Foundations of Data Science by : Jianqing Fan

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 752 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.

The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics

Author : Jeffrey Racine
Publisher : Oxford University Press
ISBN 13 : 0199857954
Total Pages : 562 pages
Book Rating : 4.1/5 (998 download)

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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 2013-12-31 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. These data-driven models seek to replace the classical parametric models of the past, which were rigid and often linear. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures. They provide a balanced view of new developments in the modeling of cross-section, time series, panel, and spatial data. Topics of the volume include: the methodology of semiparametric models and special regressor methods; inverse, ill-posed, and well-posed problems; methodologies related to additive models; sieve regression, nonparametric and semiparametric regression, and the true error of competing approximate models; support vector machines and their modeling of default probability; series estimation of stochastic processes and their application in Econometrics; identification, estimation, and specification problems in semilinear time series models; nonparametric and semiparametric techniques applied to nonstationary or near nonstationary variables; the estimation of a set of regression equations; and a new approach to the analysis of nonparametric models with exogenous treatment assignment.

Systemic Risk, Crises, and Macroprudential Regulation

Author : Xavier Freixas
Publisher : MIT Press
ISBN 13 : 0262549018
Total Pages : 487 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Systemic Risk, Crises, and Macroprudential Regulation by : Xavier Freixas

Download or read book Systemic Risk, Crises, and Macroprudential Regulation written by Xavier Freixas and published by MIT Press. This book was released on 2023-08-22 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A framework for macroprudential regulation that defines systemic risk and macroprudential policy, describes macroprudential tools, and surveys the effectiveness of existing macroprudential regulation. The recent financial crisis has shattered all standard approaches to banking regulation. Regulators now recognize that banking regulation cannot be simply based on individual financial institutions' risks. Instead, systemic risk and macroprudential regulation have come to the forefront of the new regulatory paradigm. Yet our knowledge of these two core aspects of regulation is still limited and fragmented. This book offers a framework for understanding the reasons for the regulatory shift from a microprudential to a macroprudential approach to financial regulation. It defines systemic risk and macroprudential policy, cutting through the generalized confusion as to their meaning; contrasts macroprudential to microprudential approaches; discusses the interaction of macroprudential policy with macroeconomic policy (monetary policy in particular); and describes macroprudential tools and experiences with macroprudential regulation around the world. The book also considers the remaining challenges for establishing effective macroprudential policy and broader issues in regulatory reform. These include the optimal size and structure of the financial system, the multiplicity of regulatory bodies in the United States, the supervision of cross-border financial institutions, and the need for international cooperation on macroprudential policies.

Statistical Foundations of Data Science

Author : Jianqing Fan
Publisher : CRC Press
ISBN 13 : 0429527616
Total Pages : 942 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Statistical Foundations of Data Science by : Jianqing Fan

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.

Applied Quantitative Finance

Author : Wolfgang Karl Härdle
Publisher : Springer
ISBN 13 : 3662544865
Total Pages : 369 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Applied Quantitative Finance by : Wolfgang Karl Härdle

Download or read book Applied Quantitative Finance written by Wolfgang Karl Härdle and published by Springer. This book was released on 2017-08-02 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides practical solutions and introduces recent theoretical developments in risk management, pricing of credit derivatives, quantification of volatility and copula modeling. This third edition is devoted to modern risk analysis based on quantitative methods and textual analytics to meet the current challenges in banking and finance. It includes 14 new contributions and presents a comprehensive, state-of-the-art treatment of cutting-edge methods and topics, such as collateralized debt obligations, the high-frequency analysis of market liquidity, and realized volatility. The book is divided into three parts: Part 1 revisits important market risk issues, while Part 2 introduces novel concepts in credit risk and its management along with updated quantitative methods. The third part discusses the dynamics of risk management and includes risk analysis of energy markets and for cryptocurrencies. Digital assets, such as blockchain-based currencies, have become popular b ut are theoretically challenging when based on conventional methods. Among others, it introduces a modern text-mining method called dynamic topic modeling in detail and applies it to the message board of Bitcoins. The unique synthesis of theory and practice supported by computational tools is reflected not only in the selection of topics, but also in the fine balance of scientific contributions on practical implementation and theoretical concepts. This link between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners convenient access to new techniques in quantitative finance. Hence the book will appeal both to researchers, including master and PhD students, and practitioners, such as financial engineers. The results presented in the book are fully reproducible and all quantlets needed for calculations are provided on an accompanying website. The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allows readers to reproduce the tables, pictures and calculations inside this Springer book.

Partially Linear Models

Author : Wolfgang Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 3642577008
Total Pages : 210 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Partially Linear Models by : Wolfgang Härdle

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.

New Frontiers in Bayesian Statistics

Author : Raffaele Argiento
Publisher : Springer Nature
ISBN 13 : 303116427X
Total Pages : 122 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis New Frontiers in Bayesian Statistics by : Raffaele Argiento

Download or read book New Frontiers in Bayesian Statistics written by Raffaele Argiento and published by Springer Nature. This book was released on 2022-11-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of peer-reviewed contributions to the fifth Bayesian Young Statisticians Meeting, BaYSM 2021, held virtually due to the COVID-19 pandemic on 1-3 September 2021. Despite all the challenges of an online conference, the meeting provided a valuable opportunity for early career researchers, including MSc students, PhD students, and postdocs to connect with the broader Bayesian community. The proceedings highlight many different topics in Bayesian statistics, presenting promising methodological approaches to address important challenges in a variety of applications. The book is intended for a broad audience of people interested in statistics, and provides a series of stimulating contributions on theoretical, methodological, and computational aspects of Bayesian statistics.