Abstract
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.
Highlights
Quantile regression has become a very useful tool in economics, statistics, and other social sciences
We consider a location-scale model given in (1), but differing from the existing literature, we focus on the problem of estimating the conditional quantile function of Yi given Xi = x based on a location-scale quantile model framework
To avoid calculating complicated leading bias terms in the conditional quantile estimator, we suggest using the undersmoothed smoothing parameters hj, j = 1,2, in constructing bootstrap confidence bands
Summary
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. We propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the checkfunction-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
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