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Author: Ibrahim Sidi Zakari
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Ce travail est une contribution à la sélection de modèles statistiques et plus précisément à la sélection de variables dans le cadre de régression linéaire sur les quantiles pénalisée lorsque la dimension est grande. On se focalise sur deux points lors de la procédure de sélection : la stabilité de sélection et la prise en compte de variables présentant un effet de groupe. Dans une première contribution, on propose une transition des moindres carrés pénalisés vers la régression sur les quantiles (QR). Une approche de type bootstrap fondée sur la fréquence de sélection de chaque variable est proposée pour la construction de modèles linéaires (LM). Dans la majorité des cas, l'approche QR fournit plus de coefficients significatifs. Une deuxième contribution consiste à adapter certains algorithmes de la famille « Random » LASSO (Least Absolute Solution and Shrinkage Operator) au cadre de la QR et à proposer des méthodes de stabilité de sélection. Des exemples provenant de la sécurité alimentaire illustrent les résultats obtenus. Dans le cadre de la QR pénalisée en grande dimension, on établit la propriété d'effet groupement sous des conditions plus faibles ainsi que les propriétés oracles. Deux exemples de données réelles et simulées illustrent les chemins de régularisation des algorithmes proposés. La dernière contribution traite la sélection de variables pour les modèles linéaires généralisés (GLM) via la vraisemblance nonconcave pénalisée. On propose un algorithme pour maximiser la vraisemblance pénalisée pour une large classe de fonctions de pénalité non convexes. La propriété de convergence de l'algorithme ainsi que la propriété oracle de l'estimateur obtenu après une itération ont été établies. Des simulations ainsi qu'une application sur données réelles sont également présentées.
Author: Ibrahim Sidi Zakari
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Ce travail est une contribution à la sélection de modèles statistiques et plus précisément à la sélection de variables dans le cadre de régression linéaire sur les quantiles pénalisée lorsque la dimension est grande. On se focalise sur deux points lors de la procédure de sélection : la stabilité de sélection et la prise en compte de variables présentant un effet de groupe. Dans une première contribution, on propose une transition des moindres carrés pénalisés vers la régression sur les quantiles (QR). Une approche de type bootstrap fondée sur la fréquence de sélection de chaque variable est proposée pour la construction de modèles linéaires (LM). Dans la majorité des cas, l'approche QR fournit plus de coefficients significatifs. Une deuxième contribution consiste à adapter certains algorithmes de la famille « Random » LASSO (Least Absolute Solution and Shrinkage Operator) au cadre de la QR et à proposer des méthodes de stabilité de sélection. Des exemples provenant de la sécurité alimentaire illustrent les résultats obtenus. Dans le cadre de la QR pénalisée en grande dimension, on établit la propriété d'effet groupement sous des conditions plus faibles ainsi que les propriétés oracles. Deux exemples de données réelles et simulées illustrent les chemins de régularisation des algorithmes proposés. La dernière contribution traite la sélection de variables pour les modèles linéaires généralisés (GLM) via la vraisemblance nonconcave pénalisée. On propose un algorithme pour maximiser la vraisemblance pénalisée pour une large classe de fonctions de pénalité non convexes. La propriété de convergence de l'algorithme ainsi que la propriété oracle de l'estimateur obtenu après une itération ont été établies. Des simulations ainsi qu'une application sur données réelles sont également présentées.
Author: Cristina Davino
Publisher: John Wiley & Sons
ISBN: 111997528X
Category : Mathematics
Languages : en
Pages : 288
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Book Description
A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
Author: Roger Koenker
Publisher: CRC Press
ISBN: 1351646567
Category : Mathematics
Languages : en
Pages : 739
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Book Description
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.
Author: Bernd Fitzenberger
Publisher: Springer Science & Business Media
ISBN: 3662115921
Category : Business & Economics
Languages : en
Pages : 325
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Book Description
Quantile regression has emerged as an essential statistical tool of contemporary empirical economics and biostatistics. Complementing classical least squares regression methods which are designed to estimate conditional mean models, quantile regression provides an ensemble of techniques for estimating families of conditional quantile models, thus offering a more complete view of the stochastic relationship among variables. This volume collects 12 outstanding empirical contributions in economics and offers an indispensable introduction to interpretation, implementation, and inference aspects of quantile regression.
Author: Roger Koenker
Publisher: CRC Press
ISBN: 1498725295
Category : Mathematics
Languages : en
Pages : 463
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Book Description
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.
Author:
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ISBN:
Category :
Languages : en
Pages :
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Author: Ming Zhong
Publisher:
ISBN: 9781267666772
Category :
Languages : en
Pages :
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Book Description
In both statistics and econometrics, there is a large amount of research literature on issues related to structural breaks. Since checking model stability is a long-standing problem in regression (or autoregression) models, it is desirable to develop methodsto test the presence of break points, and estimate their locations if they exist. By doing so a data series may be segmented into several subseries, which are commonly assumed to have the same functional form but dierent parameters. Another important issue in multiple regressions involves determining which covariates are to be included in the final model. In practice, it is often the case that many covariates are collected and a large parametric model is built at the initial stage. However, the inclusion of irrelevant variables may reduce model performance and stability, aggravate computational burden, and make the resultant model difficult to interpret. Thus, how to efficiently select a subset of significant covariates upon which the response variable depends is of key importance when building multiple regressionmodels. The goal of our research focuses on the above-mentioned two questions: break point detection and variable selection. In Chapter 2, we jointly address both issues in a quantile regression setting. We then elaborate on the problem of break point detection for nonstationary time series in Chapter 3. For both investigations, we emphasize the importance of utilizing quantile related models, and develop methodologies based on them. In Chapter 1, we first introduce the quantile regression model. Distinct from classical regressions in which parameter estimates are derived based on the conditional mean of the response variable given certain values of the predictor variables, quantile regressions aim at estimating either at the conditional median or other quantiles of the response variable. As time series counterpart, the quantile autoregression model is then presented, and shown to be a member of the class of random coefficient autoregressions, often used in time series analysis. We further introduce the problem of break point detection and variable selection in detail, and conduct a literature review on these two topics. As the goal is to nd the best model (either with correctly identified break points, or with appropriately selected variables, or both), the estimation criterion (based on the Minimum Description Length Principle) and the optimization algorithm (based on a Genetic Algorithm) are illustrated. In the second chapter, we propose a new procedure for simultaneously estimating the number and locations of structural breaks and conducting variable selection at conditional quantile(s). In particular, with piecewise quantile regression structure, the estimated segments with selected variables are expected to minimize a convex objective function, and a genetic algorithm is implemented to solve this optimization problem. To incorporate possibly skewed and heavy-tailed innovations into the model building process, we propose the use of Asymmetric Laplace innovations as a substitute of Gaussian innovations. We develop large sample properties and theoretical justifications for the consistency of this method. Numerical results from simulations and data applications show that the proposed approach turns out to be competitive with and often superior to a number of existing methods. The third chapter presents the approach for estimating the number and locations of break points in nonstationary time series via quantile autoregression models. The methodology and its implementation details are linked to those in Chapter 2. Asymptotic properties and theoretical justifications for the consistency of this method are derived, and several simulations as well as data applications are employed to illustrate that our method consistently estimates the number and locations of the breaks.
Author: I. Gusti Ngurah Agung
Publisher: John Wiley & Sons
ISBN: 1119715180
Category : Mathematics
Languages : en
Pages : 496
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QUANTILE REGRESSION A thorough presentation of Quantile Regression designed to help readers obtain richer information from data analyses The conditional least-square or mean-regression (MR) analysis is the quantitative research method used to model and analyze the relationships between a dependent variable and one or more independent variables, where each equation estimation of a regression can give only a single regression function or fitted values variable. As an advanced mean regression analysis, each estimation equation of the mean-regression can be used directly to estimate the conditional quantile regression (QR), which can quickly present the statistical results of a set nine QR(τ)s for τ(tau)s from 0.1 up to 0.9 to predict detail distribution of the response or criterion variable. QR is an important analytical tool in many disciplines such as statistics, econometrics, ecology, healthcare, and engineering. Quantile Regression: Applications on Experimental and Cross Section Data Using EViews provides examples of statistical results of various QR analyses based on experimental and cross section data of a variety of regression models. The author covers the applications of one-way, two-way, and n-way ANOVA quantile regressions, QRs with multi numerical predictors, heterogeneous QRs, and latent variables QRs, amongst others. Throughout the text, readers learn how to develop the best possible quantile regressions and how to conduct more advanced analysis using methods such as the quantile process, the Wald test, the redundant variables test, residual analysis, the stability test, and the omitted variables test. This rigorous volume: Describes how QR can provide a more detailed picture of the relationships between independent variables and the quantiles of the criterion variable, by using the least-square regression Presents the applications of the test for any quantile of any numerical response or criterion variable Explores relationship of QR with heterogeneity: how an independent variable affects a dependent variable Offers expert guidance on forecasting and how to draw the best conclusions from the results obtained Provides a step-by-step estimation method and guide to enable readers to conduct QR analysis using their own data sets Includes a detailed comparison of conditional QR and conditional mean regression Quantile Regression: Applications on Experimental and Cross Section Data Using EViews is a highly useful resource for students and lecturers in statistics, data analysis, econometrics, engineering, ecology, and healthcare, particularly those specializing in regression and quantitative data analysis.
Author: Gerhard Svolba
Publisher: SAS Institute
ISBN: 1635260566
Category : Computers
Languages : en
Pages : 490
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Book Description
See how data science can answer the questions your business faces! Applying Data Science: Business Case Studies Using SAS, by Gerhard Svolba, shows you the benefits of analytics, how to gain more insight into your data, and how to make better decisions. In eight entertaining and real-world case studies, Svolba combines data science and advanced analytics with business questions, illustrating them with data and SAS code. The case studies range from a variety of fields, including performing headcount survival analysis for employee retention, forecasting the demand for new projects, using Monte Carlo simulation to understand outcome distribution, among other topics. The data science methods covered include Kaplan-Meier estimates, Cox Proportional Hazard Regression, ARIMA models, Poisson regression, imputation of missing values, variable clustering, and much more! Written for business analysts, statisticians, data miners, data scientists, and SAS programmers, Applying Data Science bridges the gap between high-level, business-focused books that skimp on the details and technical books that only show SAS code with no business context.
Author: Mohammed Abdulkerim Ibrahim
Publisher:
ISBN:
Category :
Languages : en
Pages : 148
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