An Empirical Quantile Function for Linear Models with iid Errors

Bassett, Gilbert W.; Koenker, Roger

doi:10.1080/01621459.1982.10477826

Cited by 102 publications

(97 citation statements)

References 27 publications

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“…The correspondance between the random coefficient formulation of the QAR model (1) and the conditional quantile function formulation (2) presupposes the monotonicity of the latter in τ . In the region Υ where this monotonicity holds (1) can be regarded as a valid mechanism for simulating from the QAR model (2). Of course, model (1) can, even in the absence of this monotonicity, be taken as a valid data generating mechanism, however the link to the strictly linear conditional quantile model is no longer valid.…”

Section: The Modelmentioning

confidence: 99%

Quantile Autoregression

Koenker

Zhang

2006

Journal of the American Statistical Association

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534

366

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Abstract. We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale and shape of the conditional distribution of the response, and therefore constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift. The models may be interpreted as a special case of the general random coefficient autoregression model with strongly dependent coefficients. Statistical properties of the proposed model and associated estimators are studied. The limiting distributions of the autoregression quantile process are derived. Quantile autoregression inference methods are also investigated. Empirical applications of the model to the U.S. unemployment rate and U.S. gasoline prices highlight the potential of the model.

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Section: The Modelmentioning

confidence: 99%

Quantile Autoregression

Koenker

Zhang

2006

Journal of the American Statistical Association

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534

366

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“…One way of estimating F −1 (s) is to use a variant of the empirical quantile function for the linear model proposed in Bassett and Koenker (1982),…”

Section: Calculating Critical Values Usingmentioning

confidence: 99%

Unit Root Quantile Autoregression Inference

Koenker

Zhang

2004

Journal of the American Statistical Association

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405

364

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Abstract. We study statistical inference in quantile autoregression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a linear combination of the Dickey-Fuller distribution and the standard normal, with the weight determined by the correlation coefficient of related time series. Inference methods based on the estimator are investigated asymptotically. Monte Carlo results indicate that the new inference procedures have power gains over the conventional least squares based unit root tests in the presence of non-Gaussian disturbances. An empirical application of the model to US macroeconomic time series data further illustrates the potential of the new approach.

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“…The approximate regression quantiles introduced in this paper are related to the regression quantiles, introduced in [5] and [2] and then extended in a number of papers in various directions, cf [4]. The approximate regression quantiles differ from regression quantiles by using a general convex M-function instead of the absolute value function and by using correction (17).…”

Section: Discussionmentioning

confidence: 99%

“…Regression quantiles, introduced in [5] and [2], provided a method of estimation of conditional quantiles of parametric regression models. Conditional quantiles in regression models are useful to describe noncentral parts, or even upper and lower boundaries of a cloud of data points.…”

Section: Introductionmentioning

confidence: 99%

Modelling weather data by approximate regression quantiles.

Green

Kozek²

2003

ANZIAMJ

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In the paper we introduce and explore an approximate regression quantiles method. It is based on a new interpretation of M-functionals as quantiles of probability distributions which are determined by the original distribution and the Mfunction. A correction factor can be applied and this brings the corrected M-functional, called an approximate quantile functional, very close to the quantiles of the original distribution. In the present paper we extend approximate quantile functionals onto parametric models and call them approximate regression quantiles. We next model probability distributions of some weather components as they vary over time. We use very simple, but non-linear, parametric models. By applying the approximate regression quantiles method we obtain five-curve summaries of the varying over time probability distributions of the considered weather components.

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An Empirical Quantile Function for Linear Models with iid Errors

Cited by 102 publications

References 27 publications

Quantile Autoregression

Quantile Autoregression

Unit Root Quantile Autoregression Inference

Modelling weather data by approximate regression quantiles.

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