Quantile Regression

Author: Lingxin Hao
Editor: SAGE
ISBN: 9781412926287
File Size: 62,61 MB
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Quantile Regression, the first book of Hao and Naiman's two-book series, establishes the seldom recognized link between inequality studies and quantile regression models. Though separate methodological literature exists for each subject, the authors seek to explore the natural connections between this increasingly sought-after tool and research topics in the social sciences. Quantile regression as a method does not rely on assumptions as restrictive as those for the classical linear regression; though more traditional models such as least squares linear regression are more widely utilized, Hao and Naiman show, in their application of quantile regression to empirical research, how this model yields a more complete understanding of inequality. Inequality is a perennial concern in the social sciences, and recently there has been much research in health inequality as well. Major software packages have also gradually implemented quantile regression. Quantile Regression will be of interest not only to the traditional social science market but other markets such as the health and public health related disciplines. Key Features: Establishes a natural link between quantile regression and inequality studies in the social sciences Contains clearly defined terms, simplified empirical equations, illustrative graphs, empirical tables and graphs from examples Includes computational codes using statistical software popular among social scientists Oriented to empirical research

Quantile Regression

Author: Roger Koenker
Editor:
ISBN: 9781107713833
File Size: 25,65 MB
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Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Economic Applications Of Quantile Regression

Author: Bernd Fitzenberger
Editor: Springer Science & Business Media
ISBN: 3662115921
File Size: 10,11 MB
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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.

Errors In The Dependent Variable Of Quantile Regression Models

Author: Jerry A. Hausman
Editor:
ISBN:
File Size: 60,51 MB
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The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors-in-variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum-likelihood approach that is robust to left-hand side measurement error. After providing sufficient conditions for identification, we demonstrate that when the number of knots in the quantile grid is chosen to grow at an adequate speed, the sieve maximum-likelihood estimator is consistent and asymptotically normal, permitting inference via bootstrapping. We verify our theoretical results with Monte Carlo simulations and illustrate our estimator with an application to the returns to education highlighting changes over time in the returns to education that have previously been masked by measurement-error bias.

Journal Of Housing Research

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Editor:
ISBN:
File Size: 16,53 MB
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A Quantile Regression Analysis Of The Cross Section Of Stock Market Returns

Author: Michelle L. Barnes
Editor:
ISBN:
File Size: 42,92 MB
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Quantile Regression

Author: Cristina Davino
Editor: John Wiley & Sons
ISBN: 1118752716
File Size: 65,95 MB
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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.

Handbook Of Quantile Regression

Author: Roger Koenker
Editor: CRC Press
ISBN: 1498725295
File Size: 61,22 MB
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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.

Quantile Regression For Spatial Data

Author: Daniel P. McMillen
Editor: Springer Science & Business Media
ISBN: 3642318150
File Size: 28,38 MB
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Quantile regression analysis differs from more conventional regression models in its emphasis on distributions. Whereas standard regression procedures show how the expected value of the dependent variable responds to a change in an explanatory variable, quantile regressions imply predicted changes for the entire distribution of the dependent variable. Despite its advantages, quantile regression is still not commonly used in the analysis of spatial data. The objective of this book is to make quantile regression procedures more accessible for researchers working with spatial data sets. The emphasis is on interpretation of quantile regression results. A series of examples using both simulated and actual data sets shows how readily seemingly complex quantile regression results can be interpreted with sets of well-constructed graphs. Both parametric and nonparametric versions of spatial models are considered in detail.

Quantile Regression Censoring And The Structure Of Wages

Author: Gary Chamberlain
Editor:
ISBN:
File Size: 32,94 MB
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Efficient Computation And Model Selection For Regularized Quantile Regression

Author: Youjuan Li
Editor:
ISBN:
File Size: 16,65 MB
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Male And Female Wage Functions

Author: Maria da Conceição Figueiredo
Editor:
ISBN:
File Size: 64,36 MB
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Quantile Regression

Author: Marilena Furno
Editor: John Wiley & Sons
ISBN: 111886364X
File Size: 31,36 MB
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Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Bayesian Bivariate Quantile Regression

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ISBN:
File Size: 10,68 MB
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Quantile regression (QR) has become a widely used tool to study the impact of covariates on quantiles of a response distribution. QR provides a detailed description of the conditional response when considering a dense set of quantiles, without assuming a closed form for its distribution. The Bayesian version of QR, which can be implemented by considering the asymmetric Laplace distribution (ALD) as an auxiliary error distribution, is an attractive alternative to other methods because it returns knowledge on the whole parameter distribution instead of solely point estimations. While for the univariate case there has been a lot of development in the last few years, multivariate responses have only been treated to a little extent in the literature, especially in the Bayesian case. By using a multivariate version of the location scale mixture representation for the ALD, we are able to apply inference techniques developed for multivariate Gaussian models on multivariate quantile regression and make thus the impact of covariates on the quantiles of more than one dependent variable feasible. The model structure also facilitates the determination of conditional correlations between bivariate responses on different quantile levels after adjusting for covariate effects.

Quantile Regression And Extremes

Author: Raka Mandal
Editor:
ISBN:
File Size: 64,76 MB
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The estimation of conditional quantiles of a response variable is of prime interest in many statistical applications. Quantile regression (QR) is a powerful and popular method usedextensively to estimate conditional quantiles of a response Y in the presence of a covariate X. Moreover, QR can quantify the effect of covariates at different quantile levels. Whilemodeling a rare event, quantiles at high or low tails are of particular interest. In such cases, QR has inevitable shortfalls. Since we have fewer data at tails, QR estimates suffer fromhigh variability. The performance deteriorates further when the underlying distribution is heavy-tailed. Estimation of extreme quantiles is therefore challenging, especially when thedata comes from a heavy-tailed distribution.Extreme value theory (EVT) provides mathematical tools to analyze rare events. In practice, EVT can be used to assess the probability of more extreme events than any previouslyobserved occurrences. The scope of application of EVT includes financial risk assessment, extreme climate modeling, network anomaly detection, etc. Statistical modeling using EVTcan be carried out in two approaches: Block maxima and Peak over Threshold (POT). In the block maxima approach, Generalized extreme value (GEV) distribution is fitted to a seriesof maximums derived from the observations. In the POT approach, one fits Generalized Pareto (GP) distribution to observations exceeding a certain threshold.An important problem while using the POT approach is the choice of the threshold. Models based on EVT use asymptotic arguments to approximate the tail behavior. Hence,the choice of the threshold is crucial in order to fit the GP distribution to the data. POT approach is a popular tool for the estimation of extreme quantiles in heavy-tailed datawherein the excesses over a threshold are modeled as a function of the covariate X. However, the efficiency of POT is severely compromised when the threshold itself varies as a function of the covariate.This dissertation proposes an integrated approach for estimating extreme conditional quantiles from a heavy-tailed distribution. We begin with the case where the threshold doesnot vary as a function of the covariate X. Using the POT approach to model the scaled conditional excess, we propose an estimator for high conditional quantile. We establishlarge sample properties of our estimator in the context of the GP distribution. Through numerical investigations, we demonstrate the superiority of our method over QR at higherquantiles. However, this method is not adequate when the threshold itself varies as a function of the covariate X. In order to circumvent this issue, we propose an extension of ourapproach, which uses standard QR to extract information on the threshold and then model the residuals as a GP distribution with covariate dependent parameters. We establish theasymptotic properties of our method in the context of the GP distribution. Extending further, we thoroughly study the asymptotic performance of this approach for a wide class ofheavy-tailed distributions using numerical simulations. Using simulation studies, we compare our approach with existing methods used in estimation of high conditional quantiles forheavy tailed distributions. As an application, we have implemented our method for the task of precipitation downscaling with data obtained from the Vancouver International Airportweather station. We have also demonstrated how our method of covariate adaptive threshold selection can be implemented in practice.

Mathematical And Statistical Methods For Insurance And Finance

Author: Cira Perna
Editor: Springer Science & Business Media
ISBN: 9788847007048
File Size: 22,89 MB
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The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.

Quantile Regression In Risk Calibration

Author: Shih-Kang Chao
Editor:
ISBN:
File Size: 37,92 MB
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Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a stressful situation for one market participant, one likes to measure how this stress affects other factors. The CoVaR (Conditional VaR) framework has been developed for this purpose. The basic technical elements of CoVaR estimation are two levels of quantile regression: one on market risk factors; another on individual risk factor. Tests on the functional form of the two-level quantile regression reject the linearity. A flexible semiparametric modeling framework for CoVaR is proposed. A partial linear model (PLM) is analyzed. In applying the technology to stock data covering the crisis period, the PLM outperforms in the crisis time, with the justification of the backtesting procedures. Moreover, using the data on global stock markets indices, the analysis on marginal contribution of risk (MCR) defined as the local first order derivative of the quantile curve sheds some light on the source of the global market risk. -- CoVaR ; Value-at-Risk ; quantile regression ; locally linear quantile regression ; partial linear model ; semiparametric model

Quantile Regression

Author: D. W. Müller
Editor:
ISBN:
File Size: 19,87 MB
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A Comparison Between Quantile Regression And Quantile Regression Forest For Covar Estimation

Author: Francesca De Robertis
Editor:
ISBN:
File Size: 65,16 MB
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The present work is focused on the estimation of CoVaR, a measure used to quantify the effects of a financial institution or the financial system in distress, on the VaR of another financial institution. In the first part, the studied case consists of five Spanish banks, namely: BBVA, Bankia, Bankinter, CaixaBank, Santander and, in a second part, the MSCI Europe index is used to analyze the financial system effects. The used method is the Quantile Regression Forest and the results are compared with the already well-known Quantile Regression. The last part of the thesis studies the relations among the banks and the system as a network.