Nonparametric Quantile Regression Estimation With Mixed Discrete and Continuous Data
提出一种结合连续和离散核函数的局部线性平滑技术来估计条件分位数函数，使用数据驱动的交叉验证选择带宽，并推导了渐近最优性理论，模拟和实证（IMDb数据）表明方法有效。
In this article, we investigate the problem of nonparametrically estimating a conditional quantile function with mixed discrete and continuous covariates. A local linear smoothing technique combining both continuous and discrete kernel functions is introduced to estimate the conditional quantile function. We propose using a fully data-driven cross-validation approach to choose the bandwidths, and further derive the asymptotic optimality theory. In addition, we also establish the asymptotic distribution and uniform consistency (with convergence rates) for the local linear conditional quantile estimators with the data-dependent optimal bandwidths. Simulations show that the proposed approach compares well with some existing methods. Finally, an empirical application with the data taken from the IMDb website is presented to analyze the relationship between box office revenues and online rating scores. Supplementary materials for this article are available online.