Bootstrapping Quantile Regression Estimators

1995 ◽  
Vol 11 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
Quantile Regression ◽  
Limit Distribution ◽  
Asymptotic Variance ◽  
Regression Estimator ◽  
Variance Matrix ◽  
Percentile Method ◽  
Coverage Probabilities ◽  
Regression Estimators ◽  
Bootstrap Percentile ◽  
Bootstrap Distribution

The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

A Note on Bootstrapping Generalized Method of Moments Estimators

1996 ◽  
Vol 12 (1) ◽  
pp. 187-197 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
New York ◽  
Limit Distribution ◽  
Generalized Method Of Moments ◽  
Test Statistic ◽  
Percentile Method ◽  
Coverage Probabilities ◽  
Bootstrap Percentile ◽  
Nominal Coverage ◽  
Moments Estimators ◽  
Bootstrap Distribution

Recently, Arcones and Giné (1992, pp. 13–47, in R. LePage & L. Billard [eds.], Exploring the Limits of Bootstrap, New York: Wiley) established that the bootstrap distribution of the M-estimator converges weakly to the limit distribution of the estimator in probability. In contrast, Brown and Newey (1992, Bootstrapping for GMM, Seminar note) discovered that the bootstrap distribution of the GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

Bootstrap Standard Error Estimates and Inference

Econometrica ◽  
2021 ◽  
Vol 89 (4) ◽  
pp. 1963-1977 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao
Keyword(s):  
Weak Convergence ◽  
Error Estimates ◽  
Limit Distribution ◽  
Standard Error ◽  
Asymptotic Variance ◽  
Theory And Practice ◽  
Second Moment ◽  
Theoretical Literature ◽  
Bootstrap Distribution

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

scholarly journals Generalized Inference on Stress-Strength Reliability in Generalized Pareto Model

2021 ◽  
Author(s):  
Sanju Scaria ◽  
Seemon Thomas ◽  
Sibil Jose
Keyword(s):  
Simulation Studies ◽  
Strength Data ◽  
Percentile Method ◽  
Generalized Pareto ◽  
Variable Approach ◽  
Pareto Model ◽  
Coverage Probabilities ◽  
Generalized Inference ◽  
Bootstrap Percentile ◽  
Generalized Variable Approach

The article focuses on the inference of stress-strength reliability in generalized Pareto model using the generalized variable approach and bootstrap percentile method. Simulation studies are conducted to obtain expected lengths and coverage probabilities of confidence intervals constructed using the generalized variable and the bootstrap percentile methods. An example consisting of real stress-strength data is also presented for illustrative purposes.

scholarly journals Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2387
Author(s):  
Xiaoshuang Zhou ◽  
Xiulian Gao ◽  
Yukun Zhang ◽  
Xiuling Yin ◽  
Yanfeng Shen
Keyword(s):  
Quantile Regression ◽  
Asymptotic Variance ◽  
Weighted Average ◽  
Least Square ◽  
Efficient Estimation ◽  
Regression Estimator ◽  
Composite Quantile Regression ◽  
Nonparametric Function ◽  
Optimal Estimator ◽  
Better Than

In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.

High-quantile regression for tail-dependent time series

Biometrika ◽  
2020 ◽  
Author(s):  
Ting Zhang
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Limit Theorems ◽  
Tail Dependence ◽  
Serial Dependence ◽  
Response Distribution ◽  
Tail Region ◽  
Strongly Mixing ◽  
Regression Estimators ◽  
High Quantile

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.

Virtual Reference Feedback Corrective Control Based on the Closed-Loop

2014 ◽  
Vol 568-570 ◽  
pp. 1135-1138 ◽  
Author(s):  
Hong Cheng Zhou ◽  
Zhi Peng Jiang
Keyword(s):  
Closed Loop ◽  
Asymptotic Variance ◽  
Sensitivity Function ◽  
Iteration Algorithm ◽  
Signal Design ◽  
Virtual Reference ◽  
Variance Matrix ◽  
Model Match ◽  
Loop Transfer Function ◽  
Feedback Correction

Firstly two controller using the virtual reference feedback control design, at the same time considering the expectation of a given model match the closed-loop transfer function and sensitivity function, which need to be in the two objective function increases the expression in a model of the sensitivity function matching. Finally the iteration algorithm of controller parameters are obtained by mathematical method. Also the asymptotic variance matrix can be applied to the control of virtual reference feedback correction virtual signal design and controller in the process of inspection.

scholarly journals Quantile Regression with Clustered Data

2016 ◽  
Vol 5 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
João M.C. Santos Silva
Keyword(s):  
Quantile Regression ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Consistent Estimator ◽  
Regression Estimator ◽  
Finite Sample ◽  
Specification Test ◽  
Asymptotically Normal ◽  
Cluster Correlation

AbstractWe study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

scholarly journals Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Usman Shahzad ◽  
Nadia H. Al-Noor ◽  
Noureen Afshan ◽  
David Anekeya Alilah ◽  
Muhammad Hanif ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Robust Regression ◽  
Real Life ◽  
Minimum Covariance Determinant ◽  
Mean Squared Errors ◽  
Regression Estimators ◽  
Chi Squared ◽  
Class Of Estimators ◽  
The Mean ◽  
Ratio Estimators

Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.

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