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Author: Victor Chernozhukov
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 0
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Book Description
In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.
Author: Victor Chernozhukov
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 0
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Book Description
In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.
Author: Victor Chernozhukov
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors, with desirable finite sample properties and small bias. The envelope restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models, including normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The main empirical example involves a very large data-set on extramarital affairs, with high 68 percent censoring. We estimate 45-90 percent conditional quantiles. Effects of covariates are not representable as location-shifts. Less religious women, with fewer children, and higher status, tend to engage into the matters relatively more than their opposites, especially at the extremes. Marriage longevity effect is positive at moderately high quantiles and negative at high quantiles. Education and marriage happiness effects are negative, especially at the extremes. We also briefly consider the survival quantile regression on the Stanford heart transplant data. We estimate the age and prior surgery effects across survival quantiles. Keywords: Quantile regression, median regression, censoring, duration, survival, classification, discriminant analysis. JEL Classifications: C14, C24, C41, C51, D13.
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: Victor Chernozhukov
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors, with desirable finite sample properties and small bias. The envelope restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models, including normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The main empirical example involves a very large data-set on extramarital affairs, with high 68 percent censoring. We estimate 45-90 percent conditional quantiles. Effects of covariates are not representable as location-shifts. Less religious women, with fewer children, and higher status, tend to engage into the matters relatively more than their opposites, especially at the extremes. Marriage longevity effect is positive at moderately high quantiles and negative at high quantiles. Education and marriage happiness effects are negative, especially at the extremes. We also briefly consider the survival quantile regression on the Stanford heart transplant data. We estimate the age and prior surgery effects across survival quantiles.
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: Gary Chamberlain
Publisher:
ISBN:
Category : Least squares
Languages : en
Pages : 62
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Author: Moshe Buchinsky
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Chithran Vadaverkkot Vasudevan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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In Survival analysis, it is vital to understand the effect of the covariates on the survival time. Commonly studied models are the Cox [1972] proportional hazards model and the accelerated failure time model. These methods mainly focus on one characteristic of the survival time. In reality, the association between the response and risk factors is not homogeneous always. This leads to the use of quantile regression [Koenker and Basset, 1978] models, which provide a global description of the association. In quantile regression modeling of the survival data, the problem of estimating the regression coefficients for extreme quantiles can be affected by severe censoring [Portnoy, 2003], especially when the sample size is small. In epidemiological studies, however, there are often times when only a subset of the whole study cohort is accurately observed. The rest of the cohort has only some auxiliary covariate available. The naive use of the auxiliary covariate in the model without the accurately measured covariate could lead to biased estimates. To deal with this problem in censored quantile regression, we propose a regression calibration based method when there is a linear relationship between the auxiliary covariate and the accurately measured covariate. When the relationship is non-linear, we propose a non-parametric kernel smoothing technique. We also propose an empirical likelihood [Owen, 1998, 2001] based weighted censored quantile regression to improve the efficiency of the censored quantile regression estimation by utilizing the auxiliary information about the target population parameters available through scientific facts/previous studies. The proposed estimators are consistent and have asymptotically Gaussian distributions. The efficiency gain compared to the existing methods is remarkable. These methods provide the possibilities of looking into extreme quantiles of the survival distribution. We also applied our proposed methods in real case examples.
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.
