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Finite Sample Inference For Quantile Regression Models
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Book Synopsis Finite Sample Inference for Quantile Regression Models by : Victor Chernozhukov
Download or read book Finite Sample Inference for Quantile Regression Models written by Victor Chernozhukov and published by . This book was released on 2006 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference for both linear and nonlinear quantile models regardless of whether the covariates are endogenous or exogenous. The confidence regions can be computed using MCMC, and confidence bounds for single parameters of interest can be computed through a simple combination of optimization and search algorithms. We illustrate the finite sample procedure through a brief simulation study and two empirical examples: estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling. In all cases, we find pronounced differences between confidence regions formed using the usual asymptotics and confidence regions formed using the finite sample procedure in cases where the usual asymptotics are suspect, such as inference about tail quantiles or inference when identification is partial or weak. The evidence strongly suggests that the finite sample methods may usefully complement existing inference methods for quantile regression when the standard assumptions fail or are suspect. Keywords: Quantile Regression, Extremal Quantile Regression, Instrumental Quantile Regression. JEL Classifications: C1, C3.
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 463 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.
Book Synopsis Quantile Regression by : Cristina Davino
Download or read book Quantile Regression written by Cristina Davino and published by John Wiley & Sons. This book was released on 2013-10-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantile Regression with Generated Regressors by : Liqiong Chen
Download or read book Quantile Regression with Generated Regressors written by Liqiong Chen and published by . This book was released on 2018 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.
Book Synopsis Robust Inference for Panel Quantile Regression Models with Individual Fixed Effects and Serial Correlation by : Jungmo Yoon
Download or read book Robust Inference for Panel Quantile Regression Models with Individual Fixed Effects and Serial Correlation written by Jungmo Yoon and published by . This book was released on 2019 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing arbitrary temporal correlation structure within each individual. The conventional QR standard errors assuming independent outcomes can seriously underestimate the uncertainty of estimators and therefore overestimate the significance of effects when outcomes are serially correlated. This is analogous to the well-known size distortion in the OLS estimation of panel data, illustrated by Bertrand, Duflo, and Mullainathan (2004). Thus, we propose a clustered covariance matrix estimator that solves this problem in panel QR models. In addition, we develop two cluster robust tests and establish their asymptotic properties. Unlike OLS, there is no known data transformation in quantile models that effectively remove individual fixed effects, so we use recent advancements in panel QR literature to deal with the incidental parameters problem. Simulation studies show that cluster robust tests have good finite sample properties. We demonstrate the usefulness the new methods using an empirical capital structure example. The results document evidence of strong heterogeneity of the economic drivers across the conditional distribution of market debt ratio.
Book Synopsis Three Essays on Time Series Quantile Regression by : Yini Wang
Download or read book Three Essays on Time Series Quantile Regression written by Yini Wang and published by . This book was released on 2012 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers quantile regression models with nonstationary or nearly nonstationary time series. The first chapter outlines the thesis and discusses its theoretical and empirical contributions. The second chapter studies inference in quantile regressions with cointegrated variables allowing for multiple structural changes. The unknown break dates and regression coefficients are estimated jointly and consistently. The conditional quantile estimator has a nonstandard limit distribution. A fully modified estimator is proposed to remove the second-order bias and nuisance parameters and the resulting limit distribution is mixed normal. A simulation study shows that the fully modified quantile estimator has good finite sample properties. The model is applied to stock index data from the emerging markets of China and several mature markets. Financial market integration is found in some quantiles of the Chinese stock indices. The third chapter considers predictive quantile regression with a nearly integrated regressor. We derive nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes. The critical values are found to depend on both the quantile of interest and the local-to-unity parameter, which is not consistently estimable. Based on these critical values, we propose a valid Bonferroni bounds test for quantile predictability with persistent regressors. We employ this new methodology to test the ability of many commonly employed and highly persistent regressors, such as the dividend yield, earnings price ratio, and T-bill rate, to predict the median, shoulders, and tails of the stock return distribution. Chapter Four proposes a cumulated sum (CUSUM) test for the null hypothesis of quantile cointegration. A fully modified quantile estimator is adopted for serial correlation and endogeneity corrections. The CUSUM statistic is composed of the partial sums of the residuals from the fully modified quantile regression. Under the null, the test statistic converges to a functional of Brownian motions. In the application to U.S. interest rates of different maturities, evidence in favor of the expectations hypothesis for the term structure is found in the central part of the distributions of the Treasury bill rate and financial commercial paper rate, but in the tails of the constant maturity rate distribution.
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.
Book Synopsis Quantile Regression by : Marilena Furno
Download or read book Quantile Regression written by Marilena Furno and published by John Wiley & Sons. This book was released on 2018-07-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bias-corrected Quantile Regression Estimation of Censored Regression Models by : Pavel Čížek
Download or read book Bias-corrected Quantile Regression Estimation of Censored Regression Models written by Pavel Čížek and published by . This book was released on 2014 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite-sample Distribution-free Inference in Linear Median Regression Under Heteroskedasticity and Nonlinear Dependence of Unknown Form by : Elise Coudin
Download or read book Finite-sample Distribution-free Inference in Linear Median Regression Under Heteroskedasticity and Nonlinear Dependence of Unknown Form written by Elise Coudin and published by . This book was released on 2007 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantile Regression for Cross-Sectional and Time Series Data by : Jorge M. Uribe
Download or read book Quantile Regression for Cross-Sectional and Time Series Data written by Jorge M. Uribe and published by Springer Nature. This book was released on 2020-03-30 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief addresses the estimation of quantile regression models from a practical perspective, which will support researchers who need to use conditional quantile regression to measure economic relationships among a set of variables. It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature. All applications are illustrated with R.
Book Synopsis Maximum Likelihood Estimation of Misspecified Models by : T. Fomby
Download or read book Maximum Likelihood Estimation of Misspecified Models written by T. Fomby and published by Elsevier. This book was released on 2003-12-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comparative study of pure and pretest estimators for a possibly misspecified two-way error component model / Badi H. Baltagi, Georges Bresson, Alain Pirotte -- Estimation, inference, and specification testing for possibly misspecified quantile regression / Tae-Hwan Kim, Halbert White -- Quasimaximum likelihood estimation with bounded symmetric errors / Douglas Miller, James Eales, Paul Preckel -- Consistent quasi-maximum likelihood estimation with limited information / Douglas Miller, Sang-Hak Lee -- An examination of the sign and volatility switching arch models under alternative distributional assumptions / Mohamed F. Omran, Florin Avram -- estimating a linear exponential density when the weighting matrix and mean parameter vector are functionally related / Chor-yiu Sin -- Testing in GMM models without truncation / Timothy J. Vogelsang -- Bayesian analysis of misspecified models with fixed effects / Tiemen Woutersen -- Tests of common deterministic trend slopes applied to quarterly global temperature data / Thomas B. Fomby, Timothy J. Vogelsang -- The sandwich estimate of variance / James W. Hardin -- Test statistics and critical values in selectivity models / R. Carter Hill, Lee C. Adkins, Keith A. Bender -- Introduction / Thomas B Fomby, R. Carter Hill.
Book Synopsis Additive Models for Quantile Regression: Model Selection and Confidence Bandaids by : Roger Koenker
Download or read book Additive Models for Quantile Regression: Model Selection and Confidence Bandaids written by Roger Koenker and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive models for conditional quantile functions provide an attractive framework for nonparametric regression applications focused on features of the response beyond its central tendency. Total variation roughness penalities can be used to control the smoothness of the additive components much as squared Sobelev penalties are used for classical L2 smoothing splines. We describe a general approach to estimation and inference for additive models of this type. We focus attention primarily on selection of smoothing parameters and on the construction of confidence bands for the nonparametric components. Both pointwise and uniform confidence bands are introduced; the uniform bands are based on the Hotelling (1939) tube approach. Some simulation evidence is presented to evaluate finite sample performance and the methods are also illustrated with an application to modeling childhood malnutrition in India.
Book Synopsis Quantile Regression Random Effects by : Antonio F. Galvao
Download or read book Quantile Regression Random Effects written by Antonio F. Galvao and published by . This book was released on 2017 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a random effects model for quantile regression (QR). We establish identification of the QR coefficients, and develop practical estimation and inference procedures. We employ a simple pooled QR estimator to estimate the coefficients of interest, and derive its statistical properties. The random effects induce cluster dependence hence we use a cluster-robust variance-covariance matrix estimator for inference, and establish its uniform consistency over the set of quantiles. We also develop a new test procedure for uniform testing of linear hypotheses in QR models. This procedure is a modified Wald test applied on a growing number of quantiles such that, asymptotically, the test is uniform over the quantiles. We show this procedure can be applied to test the random effects hypothesis in QR panel data models. Two significant differences between our model and fixed-effects QR models are that effects of time-invariant regressors can be estimated, and that the time-series dimension can be small and finite. We provide Monte Carlo simulations to evaluate the finite sample performance of the estimation and inference procedures. Finally, we apply the proposed methods to study the roles of education and ability in wage determination. We document strong heterogeneity in returns to education along the conditional distribution of earnings.
Book Synopsis Quantile Regression by : Marilena Furno
Download or read book Quantile Regression written by Marilena Furno and published by Wiley. This book was released on 2018-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantile Regression by : Lingxin Hao
Download or read book Quantile Regression written by Lingxin Hao and published by SAGE Publications. This book was released on 2007-04-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Quantile Regression by : Roger Koenker
Download or read book Quantile Regression written by Roger Koenker and published by Cambridge University Press. This book was released on 2005-05-05 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
