scholarly journals Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

2011 ◽  
Vol 2011 ◽  
pp. 1-35
Author(s):  
Sidi Ali Ould Abdi ◽  
Sophie Dabo-Niang ◽  
Aliou Diop ◽  
Ahmedoune Ould Abdi
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Quantile Function ◽  
Spatial Process ◽  
Kernel Estimate ◽  
Conditional Quantile ◽  
Conditional Quantile Estimator ◽  
Conditional Quantile Function ◽  
Mixing Sequence ◽  
Explicative Variable

Given a stationary multidimensional spatial process , we investigate a kernel estimate of the spatial conditional quantile function of the response variable given the explicative variable . Asymptotic normality of the kernel estimate is obtained when the sample considered is an -mixing sequence.

scholarly journals Nonparametric Estimation of a Conditional Quantile Function in a Fixed Effects Panel Data Model

2018 ◽  
Vol 11 (3) ◽  
pp. 44 ◽  
Author(s):  
Karen Yan ◽  
Qi Li
Keyword(s):  
Panel Data ◽  
Data Model ◽  
Numerical Optimization ◽  
Fixed Effects ◽  
Quantile Function ◽  
Panel Data Model ◽  
Nonparametric Method ◽  
Conditional Quantile ◽  
Finite Samples ◽  
Conditional Quantile Function

This paper develops a nonparametric method to estimate a conditional quantile function for a panel data model with an additive individual fixed effects. The proposed method is easy to implement, it does not require numerical optimization and automatically ensures quantile monotonicity by construction. Monte Carlo simulations show that the proposed estimator performs well in finite samples.

qmodel: A command for fitting parametric quantile models

2019 ◽  
Vol 19 (2) ◽  
pp. 261-293 ◽  
Author(s):  
Matteo Bottai ◽  
Nicola Orsini
Keyword(s):  
Quantile Regression ◽  
Simulated Data ◽  
Quantile Function ◽  
Parametric Models ◽  
Outcome Variable ◽  
Simple Type ◽  
Conditional Quantile ◽  
Quantile Functions ◽  
Conditional Quantile Function ◽  
Insight Into

In this article, we introduce the qmodel command, which fits parametric models for the conditional quantile function of an outcome variable given covariates. Ordinary quantile regression, implemented in the qreg command, is a popular, simple type of parametric quantile model. It is widely used but known to yield erratic estimates that often lead to uncertain inferences. Parametric quantile models overcome these limitations and extend modeling of conditional quantile functions beyond ordinary quantile regression. These models are flexible and efficient. qmodel can estimate virtually any possible linear or nonlinear parametric model because it allows the user to specify any combination of qmodel-specific built-in functions, standard mathematical and statistical functions, and substitutable expressions. We illustrate the potential of parametric quantile models and the use of the qmodel command and its postestimation commands through realand simulated-data examples that commonly arise in epidemiological and pharmacological research. In addition, this article may give insight into the close connection that exists between quantile functions and the true mathematical laws that generate data.

scholarly journals ON USING LINEAR QUANTILE REGRESSIONS FOR CAUSAL INFERENCE

2016 ◽  
Vol 33 (3) ◽  
pp. 664-690 ◽  
Author(s):  
Ryutah Kato ◽  
Yuya Sasaki
Keyword(s):  
Causal Inference ◽  
Unobserved Heterogeneity ◽  
Weighted Average ◽  
Quantile Function ◽  
Structural Function ◽  
Slope Parameter ◽  
Quantile Regressions ◽  
Conditional Quantile ◽  
Conditional Quantile Function ◽  
Linear Regressions

We show that the slope parameter of the linear quantile regression measures a weighted average of the local slopes of the conditional quantile function. Extending this result, we also show that the slope parameter measures a weighted average of the partial effects for a general structural function. Our results support the use of linear quantile regressions for causal inference in the presence of nonlinearity and multivariate unobserved heterogeneity. The same conclusion applies to linear regressions.

Consistency of a nonparametric conditional quantile estimator for random fields

2010 ◽  
Vol 19 (1) ◽  
pp. 1-21 ◽  
Author(s):  
S. A. Ould Abdi ◽  
S. Dabo-Niang ◽  
A. Diop ◽  
A. Ould Abdi
Keyword(s):  
Random Fields ◽  
Conditional Quantile ◽  
Conditional Quantile Estimator

scholarly journals NONPARAMETRIC WEIGHTED AVERAGE QUANTILE DERIVATIVE

2021 ◽  
pp. 1-39
Author(s):  
Ying-Ying Lee
Keyword(s):  
Linear Models ◽  
Weighted Average ◽  
Linear Representation ◽  
Quantile Function ◽  
Structural Effect ◽  
Compact Set ◽  
Conditional Quantile ◽  
Partially Linear ◽  
Conditional Quantile Function ◽  
Quantile Processes

The weighted average quantile derivative (AQD) is the expected value of the partial derivative of the conditional quantile function (CQF) weighted by a function of the covariates. We consider two weighting functions: a known function chosen by researchers and the density function of the covariates that is parallel to the average mean derivative in Powell, Stock, and Stoker (1989, Econometrica 57, 1403–1430). The AQD summarizes the marginal response of the covariates on the CQF and defines a nonparametric quantile regression coefficient. In semiparametric single-index and partially linear models, the AQD identifies the coefficients up to scale. In nonparametric nonseparable structural models, the AQD conveys an average structural effect under certain independence assumptions. Including a stochastic trimming function, the proposed two-step estimator is root-n-consistent for the AQD defined by the entire support of the covariates. To facilitate tractable asymptotic analysis, a key preliminary result is a new Bahadur-type linear representation of the generalized inverse kernel-based CQF estimator uniformly over the covariates in an expanding compact set and over the quantile levels. The weak convergence to Gaussian processes applies to the differentiable nonlinear functionals of the quantile processes.

Testing exogeneity in nonparametric instrumental variables models identified by conditional quantile restrictions

2020 ◽  
Author(s):  
Jia-Young Michael Fu ◽  
Joel L Horowitz ◽  
Matthias Parey
Keyword(s):  
Quantile Regression ◽  
Instrumental Variables ◽  
Regression Models ◽  
Quantile Function ◽  
Structural Function ◽  
Conditional Quantile ◽  
Explanatory Variables ◽  
Monte Carlo Experiments ◽  
Nonparametric Estimates ◽  
Conditional Quantile Function

Summary This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics. As with mean-regression models, an erroneous assumption that the explanatory variables in a quantile regression model are exogenous can lead to highly misleading results. In addition, a test of exogeneity based on an incorrectly specified parametric model can produce misleading results. This paper presents a test of exogeneity that does not assume that the structural function belongs to a known finite-dimensional parametric family and does not require estimation of this function. The latter property is important because nonparametric estimates of the structural function are unavoidably imprecise. The test presented here is consistent whenever the structural function differs from the conditional quantile function on a set of nonzero probability. The test has nontrivial power uniformly over a large class of structural functions that differ from the conditional quantile function by $O({n^{ - 1/2}})$. The results of Monte Carlo experiments and an empirical application illustrate the performance of the test.

scholarly journals A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

2021 ◽  
pp. 1-31
Author(s):  
Zheng Fang ◽  
Qi Li ◽  
Karen X. Yan
Keyword(s):  
Mean Squared Error ◽  
Bootstrap Method ◽  
Quantile Function ◽  
Confidence Bands ◽  
Convergence Theory ◽  
Conditional Quantile ◽  
Nonparametric Approach ◽  
Coverage Probabilities ◽  
Adequate Coverage ◽  
Conditional Quantile Function

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

scholarly journals A Bayesian Quantile Modeling for Spatiotemporal Relative Risk: An Application to Adverse Risk Detection of Respiratory Diseases in South Carolina, USA

2018 ◽  
Vol 15 (9) ◽  
pp. 2042 ◽  
Author(s):  
Chawarat Rotejanaprasert ◽  
Andrew Lawson
Keyword(s):  
South Carolina ◽  
Relative Risk ◽  
Great Influence ◽  
Real Data ◽  
Quantile Function ◽  
Conditional Quantile ◽  
Ordinary Regression ◽  
Health Studies ◽  
Conditional Quantile Function ◽  
Respiratory Conditions

Quantile modeling has been seen as an alternative and useful complement to ordinary regression mainly focusing on the mean. To directly apply quantile modeling to areal data the discrete conditional quantile function of the data can be an issue. Although jittering by adding a small number from a uniform distribution to impose pseudo-continuity has been proposed, the approach can have a great influence on responses with small values. Thus we proposed an alternative to model the quantiles of relative risk for spatiotemporal areal health data within a Bayesian framework using the log-Laplace distribution. A simulation study was conducted to assess the performance of the proposed method and examine whether the model could robustly estimate quantiles of spatiotemporal count data. To perform a test with a real data example, we evaluated the potential application of clustering under the proposed log-Laplace and mean regression. The data were obtained from the total number of emergency room discharges for respiratory conditions, both infectious and non-infectious diseases, in the U.S. state of South Carolina in 2009. From both simulation and case studies, the proposed quantile modeling demonstrated potential for broad applicability in various areas of spatial health studies including anomaly detection.

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